Linear Algebra
part 3 of 3
A total of 50 hours of lectures
This is an academic level course for university and college engineering. Due to its size, it is divided into three parts. This page describes the third of those three parts.
Level - Intermediate
- High-school and college mathematics (mainly arithmetics, some trigonometry, polynomials)
- Linear Algebra and Geometry 1 (systems of equations, matrices and determinants, vectors and their products, analytic geometry of lines and planes)
- Linear Algebra and Geometry 2 (vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors, diagonalization)
-
Some basic calculusBasic knowledge of complex numbers (this course contains a short introduction to complex numbers)
Curriculum
Make sure that you check with your professor what parts of the course you will need for your exam. Such things vary from country to country, from university to university, and they can even vary from year to year at the same university.
Linear Algebra, part 3 of 3
Get the outline
A detailed list of all the lectures in part 3 of the course, including which theorems will be discussed and which problems will be solved. If you are looking for a particular kind of problem or a particular concept, this is where you should look first.
Get Linear Algebra part 3 on Udemy
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Course Objectives & Outcomes for part 3
How to solve problems in linear algebra and geometry (illustrated with 144 solved problems) and why these methods work.
Use diagonalization of matrices for solving various problems from different branches of mathematics (ODE, dynamical systems).
Work with geometric concepts as length (norm), distance, angles, and orthogonality in non-geometric setups.
Orthogonal and orthonormal bases, and Gram-Schmidt process in various inner product spaces.
Symmetric matrices and their properties; orthogonal diagonalization: how it is done and how to understand it geometrically.
Quadratic forms and their connection to symmetric matrices: uniqueness of this correspondence and its consequences.
Some concepts from abstract algebra: group, ring, field, and isomorphism; understand the concept of isomorphic vector spaces.
Note: all the vector spaces discussed in this course are spaces over R (not over the field of complex numbers), and all our matrices have only real entries.
Solve more advanced problems on eigendecomposition and orthogonality than in the second course.
Inner product spaces different from R^n: space of continuous functions, spaces of polynomials, spaces of matrices.
Pythagorean Theorem, Cauchy-Schwarz inequality, and triangle inequality in various inner product spaces.
Min-max problems using Cauchy-Schwarz inequality, Best Approximation Theorem, least squares solutions.
Positive/negative definite matrices, indefinite matrices; various methods of determining definiteness of matrices.
Geometry of quadratic forms in two and three variables: conic sections and quadratic surfaces.
Crowning of the course and a natural consequence of all the other topics: Singular Value Decomposition and pseudoinverses.
Reviews (36)
Anurag P.
Udemy student
Excellent teaching style, loved the course, must recommend
Ilir S.
Udemy student
Simply amazing! I just finished the entire Linear Algebra trilogy and I have fallen in love with Math! Thanks Hania for your efforts.
Adam G.
Udemy student
All of Hania's Linear Algebra courses have been excellent. I completed my engineering education years ago without taking any courses specifically in linear algebra. During that time I learned what I needed to know to solve the problems at hand, which gave me some knowledge but I was lacking in deeper theoretical understanding. These courses have been very interesting for me and gave insight into what all the calculations are actually doing and *why* they are done the way that they are.
Gabriel G.
Udemy student
One of the best math teachers I've come across!
Anonymized User
Udemy student
Thank You Very Muxh , Dear Professor Hania.
Thank You For The Courses.
2^Infinity Love From Pakistan !
Thank You For The Courses.
2^Infinity Love From Pakistan !
Vasanth G.
Udemy student
thank you for the effort you have put to make these videos, I am enjoying the process of learning
Matteo M.
Udemy student
The course offers very interesting lectures, detailed and well-organised.
Mathematics is partly theory (philosophy) and partly "mechanics" of calculation. Without the mechanics of calculation, it remains abstract; without the theoretical part, understanding is lacking. That is why it is very important to exercise. Practice allows theory to become a technical skill and mechanics to acquire meaning.
Better if listened to with voice speed regulated x1.25 or x1.5.
Note: Section 2, Video 9 time 17.06 .. the automatic VTT .. " ... So then I will simply get back my vector by Arthur. " Do not thrust the text.
Mathematics is partly theory (philosophy) and partly "mechanics" of calculation. Without the mechanics of calculation, it remains abstract; without the theoretical part, understanding is lacking. That is why it is very important to exercise. Practice allows theory to become a technical skill and mechanics to acquire meaning.
Better if listened to with voice speed regulated x1.25 or x1.5.
Note: Section 2, Video 9 time 17.06 .. the automatic VTT .. " ... So then I will simply get back my vector by Arthur. " Do not thrust the text.
Richard H.
Udemy student
If you've already taken any of Hania's courses, then this will be beating a dead horse because you already know you can expect high quality.
Linear Algebra and Geometry 3 resumes right where part 2 leaves off, further building your intuition surrounding matrix diagonalization and eigenvectors. She touches on several useful auxiliary topics including an introduction to some abstract algebra concepts, solving systems of ODEs, difference equations, and more. As in my reviews for parts 1 and 2, I can't recommend this course enough.
Linear Algebra and Geometry 3 resumes right where part 2 leaves off, further building your intuition surrounding matrix diagonalization and eigenvectors. She touches on several useful auxiliary topics including an introduction to some abstract algebra concepts, solving systems of ODEs, difference equations, and more. As in my reviews for parts 1 and 2, I can't recommend this course enough.
Francisco O.
Udemy student
There many pros in this course many examples and lot of formal proofs.
Graphical material is provided to clarifies the concepts in the course. The only con is that is a bit large. That is not a problem if you take the time to watch the videos. There are a lot of interplay between computations and theory. A great course. I want to make a suggestion, I wonder how plausible will be a series of Advance Linear Algebra.
That is all, I know Hania has yet her schedule of courses so my suggestion is for the long run. Thanks
Graphical material is provided to clarifies the concepts in the course. The only con is that is a bit large. That is not a problem if you take the time to watch the videos. There are a lot of interplay between computations and theory. A great course. I want to make a suggestion, I wonder how plausible will be a series of Advance Linear Algebra.
That is all, I know Hania has yet her schedule of courses so my suggestion is for the long run. Thanks
Tracy
Udemy student
Perfect match. It made it easy to understand.
Moving onto Multicalculus 3/ part 1 and 2.
Thanks Hannah and Martin Wehlou.
Moving onto Multicalculus 3/ part 1 and 2.
Thanks Hannah and Martin Wehlou.
Abdel R.
Udemy student
overall amazing course, i would highly recommend this course to anyone interested in linear algebra it's offers valuable insights and skills that are directly applicable to both personal and professional growth
Daniel S.
Udemy student
It's a good course, to which a lot of work and care has been devoted.
Nikolas P.
Udemy student
She delivers so much material, her level of commitment is just crazy.
Keivan S.
Udemy student
Hania is incredibly knowledgeable and has a talent for teaching difficult concepts in an easy-to-understand manner. Her ability to break down complex ideas into simpler parts makes learning both enjoyable and effective. Highly recommended for anyone looking to master challenging subjects!
Jim W.
Udemy student
This is a terrific course.
Adil H.
Udemy student
Words can't justify how good this course is , so lets try a different way
Theorem: The course taken yields an excellent experience.
Proof:
Let
C denote the course taken.
Suppose
C encompasses a comprehensive set of topics denoted by
T.
Let
E be the experience gained from
C.
We assert that
E is excellent, i.e.,
=Excellent
E=Excellent.
By the completeness property of
C, all essential concepts and methodologies are covered.
Furthermore, the pedagogical approach employed in
C fosters deep understanding and retention of knowledge.
Therefore, by definition, the course taken (
C) provides an excellent experience (
=
Excellent
E=Excellent)
Theorem: The course taken yields an excellent experience.
Proof:
Let
C denote the course taken.
Suppose
C encompasses a comprehensive set of topics denoted by
T.
Let
E be the experience gained from
C.
We assert that
E is excellent, i.e.,
=Excellent
E=Excellent.
By the completeness property of
C, all essential concepts and methodologies are covered.
Furthermore, the pedagogical approach employed in
C fosters deep understanding and retention of knowledge.
Therefore, by definition, the course taken (
C) provides an excellent experience (
=
Excellent
E=Excellent)
Manfred K.
Udemy student
like courses 1 and 2 of Linear Algebra and Geomeetry:wonderful, patient detailed problem solutions.
Bklau
Udemy student
The strength of this course is the many solved problems presented in various examples and from different angles.
Additionally a striking balance between theory and practical computations.
Additionally a striking balance between theory and practical computations.
Matthew T.
Udemy student
Completed course linear algebra course 2 and gained very useful information. She needs to make a course 4. And she needs to obtain an applied course in linear algebra.
Covered some topics in the third course that have no geometric interpretation.
Covered some topics in the third course that have no geometric interpretation.
Andrea T.
Udemy student
This course is exceptional, like the first and second course of this series. The many solved problems deepen the understanding of the very clearly explained theory. Everthing is put into context and into a bigger picture so that with help of this course, you gain understanding of the topic on all levels. Thank you very much Hania for this wonderful experience. I'm awaiting your next courses.
Anonymized User
Udemy student
Good
Alex
Udemy student
Absolutely loved this course! I had also taken the previous two. Hania explains things in such detail showing both clear logical reasoning and geometrical intuition. She does a great job of only using terms/methods/proofs that she explained previously.
All knowledge builds upon previous content. It is very well structured with plenty of solved problems. She doesn't overwhelm you with math symbols and instead focuses on concepts.
For any problem, I found it helpful to pause the video and solve it myself before resuming to see her formulate the solution.
This is a quality course that will give you a ground up understanding of linear algebra. I'm glad there are more videos to come!
All knowledge builds upon previous content. It is very well structured with plenty of solved problems. She doesn't overwhelm you with math symbols and instead focuses on concepts.
For any problem, I found it helpful to pause the video and solve it myself before resuming to see her formulate the solution.
This is a quality course that will give you a ground up understanding of linear algebra. I'm glad there are more videos to come!
Alfonso C.
Udemy student
Bien detallado el curso. Aprendí mucho e incluso algunos conceptos que antes no los tenía muy claros.Machine translation: The course was very detailed. I learned a lot, including some concepts that I hadn't quite understood before.
Derick C.
Udemy student
I am pretty thankful for COVID-19 as it allowed professor Hania to be able to explore the idea of using tech to record high-quality lectures in mathematics: a crucial subject in pretty much everything we do. I love maths since school but the level of rigor was lacking. Even though I could get the picture of the mathematical idea, I felt something that kept bumping up in my head and bothering me. I revised lots of books. But at some point, the notation and level of detail became a nightmare to me. Then, I decided to go for free online courses. I found MIT OpenCourseWare. First, I took chemistry. I loved it as I could understand nearly everything. Then, I enrolled at Single Variable Calculus, but I felt at some level the rigor and exercises were simple. Finally, I took Multivariable Calculus. The course was great. I did understand the concepts and did a lot of exercises. Nonetheless, when I grabbed an MVC book the concepts contained a lot of notation and mathematical details I could not get my head around. Furthermore, if I got stuck, I gave up even after doing lots of research because of the complexity and time issues .... I panicked. So I try to find more rigorous courses in mathematics. But this time in Linear Algebra with Professor Hania. Now, I am more confident in that sense. The lectures are also well structured and geometrical pictures are richer and more meaningful than ever. Feedback is also there at your disposal so you can feel you can master a topic you were doubtful about even before starting. Now, I appreciate maths in more depth than ever. Last but not least, I am no longer afraid of grabbing an advanced book and setting out to understand it. I know the dynamics of how mathematics works at a high level. Thanks, professor Hania from the bottom of my heart. Words are not enough to describe my gratitude.
Salvador T.
Udemy student
Excelente presentación y didácticaMachine translation: Excellent presentation and teaching style
Murat F.
Udemy student
Best courses I took about the linear algebra (including the ones I took at the school). Anyone interested in topics should definitely enroll these courses (the Linear Algebra series by Prof Hania).
As an engineering student these lectures made me interested even in the more theoretical parts. I'll definitely learn more about linear algebra, since these courses gave me great foundations.
The instructor is very knowledgeable and polite (gives great feedback even to my most stupid questions 🙂 ). I thank both instructors for their great effort on these courses, and look forward to their next courses!
As an engineering student these lectures made me interested even in the more theoretical parts. I'll definitely learn more about linear algebra, since these courses gave me great foundations.
The instructor is very knowledgeable and polite (gives great feedback even to my most stupid questions 🙂 ). I thank both instructors for their great effort on these courses, and look forward to their next courses!
Jennifer D.
Udemy student
This really helped me get through my linear algebra unit at uni by providing lots of examples and providing all the 'in between' steps my lecturer skips over.
Maciej K.
Udemy student
Great course. Advanced and exciting topics.
Samir A.
Udemy student
Explanation is concise and clear , Instructor is extremely helpful and active in clearing the doubts. I am glad i enrolled this course.
Alp Ö.
Udemy student
Hania Hocamın 1. ve 2. kursunu bitirdim.
Harika bir hoca ve harika bir insan.
İlk iki kurs bana çok şey kattı,
Bu kursun da bana çok şey katacağından eminim.Machine translation: I’ve completed Professor Hania’s first and second courses.
She’s a wonderful teacher and a wonderful person.
The first two courses taught me a lot,
and I’m sure this course will teach me a lot as well.
Harika bir hoca ve harika bir insan.
İlk iki kurs bana çok şey kattı,
Bu kursun da bana çok şey katacağından eminim.Machine translation: I’ve completed Professor Hania’s first and second courses.
She’s a wonderful teacher and a wonderful person.
The first two courses taught me a lot,
and I’m sure this course will teach me a lot as well.
Bernard X.
Udemy student
Parfait pour moi. Je pense avoir beaucoup appris avec beaucoup de plaisir.Machine translation: Perfect for me. I think I learned a lot and really enjoyed it.
Wanda W.
Udemy student
This third course is definitely harder than the first and the second, but many illustrations and examples make it easy to follow and understand the content anyway. Hania explains all the details very clearly. The final part about SVD was really exciting.
Terrence L.
Udemy student
Professor Hania keeps me wanting to learn more from her! Great Experience!
Tetyana M.
Lecturer
The present is a logical continuation of two earlier courses by Hania, and it is presented in the same spirit – extremely carefully and in detail. It bridges elementary linear algebra with its most standard mathematical applications, motivating the students to further study both. Noteworthy here are applications under the heading of singular value decomposition, basic for what may be called linear data analysis, key to engineering and statistical computations. A warmly recommended course, for prospective data analysts not least.
Richard B.
Lecturer
This extends Hania's courses one and two with the same title, and it should be the most useful in terms of applications. It also is the hardest to present, if to follow the explicit style of the predecessors. Some abstraction is inevitable, handled carefully enough, but time is mostly spent explaining ideas and examining examples. The lectures are as easy to follow as any lectures could be, perhaps deceptively so, for some ideas are subtle. The students willing to listen and spend some time with the problems will be richly rewarded.
Andrzej P.
Udemy student
Incredible lectures! So many important topics covered in such a clear and structured manner. The exercises were especially helpful in understanding the theory and how to use it. Really helpful. Highly recommend these lectures.