Linear Algebra
part 2 of 3

A total of almost 47 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 second of those three parts.

Prerequisites

  • Linear Algebra and Geometry 1 (systems of equations, matrices and determinants, vectors and their products, analytic geometry of lines and planes)
  • High-school and college mathematics (mainly arithmetics, some trigonometry, polynomials)
  • Some basic calculus (used in some examples)
  • Basic knowledge of complex numbers (used in an example)

    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 2 of 3

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    Get the outline

    A detailed list of all the lectures in part 2 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 2 on Udemy

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    Course Objectives & Outcomes for part 2

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    How to solve problems in linear algebra and geometry (illustrated with 153 solved problems) and why these methods work.
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    Linear combinations, linear dependence and independence in various vector spaces, and how to interpret them geometrically in R^2 and R^3.
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    Row space, columns space and nullspace for matrices, and about usage of these concepts for solving various types of problems.
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    How to compose linear transformations and how to compute their standard matrices in different bases; compute the kernel and the image for transformations.
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    Work with various geometrical transformations in R^2 and R^3, be able to compute their matrices and explain how these transformations work.
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    Transform any given basis for a subspace of R^n into an orthonormal basis of the same subspace with help of Gram-Schmidt Process.
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    Determine whether a given matrix is diagonalizable or not, and perform its diagonalization if it is.
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    Use diagonalization for problem solving involving computing the powers of square matrices, and motivate why this method works.
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    Use Wronskian to determine whether a set of smooth functions is linearly independent or not; be able to compute Vandermonde determinant.
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    Important concepts concerning vector spaces, such as basis, dimension, coordinates, and subspaces.
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    How to recalculate coordinates from one basis to another, both with help of transition matrices and by solving systems of equations.
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    Linear transformations: different ways of looking at them (as matrix transformations, as transformations preserving linear combinations).
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    Understand the connection between matrices and linear transformations, and see various concepts in accordance with this connection.
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    Understand the concept of isometry and be able to give some examples, and formulate their connection with orthogonal matrices.
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    Compute eigenvalues, eigenvectors, and eigenspaces for a given matrix, and give geometrical interpretations of these concepts.
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    Understand the relationship between diagonalizability and dimensions of eigenspaces for a matrix.
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    Be able to formulate and use The Invertible Matrix Theorem and recognise the situations which are suitable for the determinant test (and which are not).
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    Work with various vector spaces, for example with R^n, the space of all n-by-m matrices, the space of polynomials, the space of smooth functions.

    Jamieson P.

    Udemy student

    I struggled with linear algebra in college and have always felt sad I could not grasp the material.

    These lectures are a treat and a joy. Thank you so much for your contribution to mathematics and education.

    Derick B.

    Udemy student

    This course is a continuation to Linear Algebra 1 . The topics covered here are offered with in-depth explanation and lots of exercises along the way. Each section is a real joy. You will learn a plethora of things which are normally tough to grasp and besides be able to connect it all. At bottom, everything in linear algebra is connected and this course fulfills the purpose.

    What’s more, textbooks require lots of dedication and sometimes the math behind it is difficult to grasp in terms of vocabulary, proofs, connections. It all sums up to being a nightmare.While this course tackles it all with less pain but same benefits are obtained. It brings tangible hope. You just need to be dedicated and disciplined in your learning. Professor Hania will do the rest. Believe me, it is worthy.

    On top of that, any online course just touches the surface of the topic and it is not rigorous even though they might be good at delivering the big picture and analogies to understand, but you keep asking what’s behind the black box. Indeed,professor Hania covers nearly all details, the big picture … and if your have a question, she offers quick in-depth feedback not only in this course but all courses she delivers.

    I am really pleased I found professor Hania!

    Justin M.

    Udemy student

    Much like the Linear Algebra 1 course, this course contains very thorough explanations of the information with lots of worked examples. I’m only to lecture 37, but up to this point, material from the first course is more clear (particularly the subspaces material, for me). I really enjoy her teaching.

    Rajarshi M.

    Udemy student

    Gonna be honest it’s probably the best way to learn linear algebra in an efficient and fast way if u give it effort and follow the problems (as in doing it before u watch the solution ) and the basic intuition and important abstractions are presented in a systematic way which will make math profs cry. Having all of the courses is a bonus as it flows really well very well.

    Is it worth the money ? honestly, yes id buys it at full price without even thinking about it.

    Hamish

    Udemy student

    I teach high school mathematics, sometimes touching on 1st year year university topics. This course is very thorough: I did about 75% of it as not all of it was relevant to my level. Hania is an excellent instructor and I look forward to doing other courses with her.

    Murat F.

    Udemy student

    Best Linear Algebra courses I took. Everything is clearly explained and proved in the lectures. Also, the instructor makes every effort to clear your doubts and help you. After completing these courses, most of the subjects in the machine learning seem very intuitive. I definitely recommend this series to anyone who wants to learn linear algebra.

    Udemy User

    Udemy student

    This course is the best on the internet—absolutely in-depth treatment of all topics pertaining to Linear Algebra. Prof. Wehlou has a knack for excitingly explaining things, and the lectures are a treasure mine when compared to other lectures (such as Prof. Strang, Prof. Pavel etc.). Waiting for all your other courses.

    Alok K.

    Udemy student

    This has been an amazing course, making learning Linear Algebra a lot of fun! I would highly recommend it to everyone. Thank you!

    Andrea T.

    Udemy student

    This course is extraordinary, like the first one as well. Topics are explained very well, from different angles and are always put in greater context. The many solved problems deepen the understandig and make you feel comfortable with the subjects. I absolutely recommend this course. It was a pleasure to watch and work through.

    Cyrus

    Udemy student

    One of the best courses on linear algebra. I look forward to each video and it makes linear algebra learning fun.

    Pierre

    Udemy student

    This course is blissful !!!

    Bernard X.

    Udemy student

    Parfait pour moi.

    Karim M.

    Udemy student

    Another great course I proudly finished ( at least at 94% cause I skipped some proofs and other stuff to which I’ll come back later). I simply love how these lectures train your brain and help you become a free thinker. I don’t know how I could live without watching these awesome lectures. I’m going to a pilot school very soon (if not a mechanical engineering school). I’m sure these lectures have helped gain a lot more maturity, critical thinking and intelligence that are needed more my studies and career. I still have the two calculus 3 courses to watch to keep me busy and prepared. I can’t wait for all the other courses (precalc, calculus 1&2, linear algebra 3…) Many thanks Hania.

    Sureshkumar M S.

    Udemy student

    After finishing part1 of this course, I took this part2 and completed in a week. Similar to part1, this part was also excellent. The structure of the course, ordering of chapters, choice of worked out problems from diverse topics, intuition behind the hard concepts were very well planned ensuring students understand easily. I loved particularly the chapters on diagonalization, Gram-Schmidt algorithm, Eigen values and Vectors, change of basis. All the topics are handled as byte sized chunks for easy understanding. Thanks to Professor for putting together this excellent course Go for it!!!

    Christer Oscar K.

    Professor mathematics

    Yes, amazing, but as expected, since this is the fourth course by Hania that I have followed. Indeed, I can only reiterate my words from the earlier ratings: this is a true masterpiece. A True Masterpiece. This applies to the planning, to the introduction explaining to the students what they are about to learn, to the process of dividing the whole theory and its concepts into units, to the presentation with a friendly way of talking and explaining easy and difficult concepts, proofs, and more or less complicated figures and diagrams. So, all in all, a true masterpiece. I do hope many students will join.

    Muhammad A.

    Udemy student

    The lectures are great with a good pace for accumulative assimilation Slides are also well-organised.

    Richard B.

    Lecturer mathematics

    This course succeeds Hania’s Linear Algebra and Geometry 1, and it is presented equally carefully. It centers on the core fact that the minimal generating sets for a linear space – the bases for the space – exist and are all of the same cardinality, and hence that the study of linear transformations, and then of the geometric objects that these transformations define, reduces to a calculus of matrices. Hania explains everything to perfection, always helping the logic with handy examples and geometric illustrations, smoothly and impressively detailed.

    Damian K.

    Udemy stuent

    Great course, very carefully planned, well explained, and with a lot of good examples to ensure you understand the concepts and develop much needed intuition.

    And if you are coming back to refresh your memory on some of these topics, you will find the structure very helpful, too.

    Tetyana M.

    Lecturer mathematics

    The logical simplicity of linear algebra could easily be disappointing had it not been for the effectiveness of linear computation. This course profiles the intuitive linear concepts in the computational direction, especially towards the algebra of matrices. The course obviously introduces new material, but it also much helps to practice the ideas and techniques previously acquired. Hania does an excellent job making complicated things look simple. A great course!