Linear Algebra - Lecture 15: A Catalog of Linear Transformations

We introduce several geometrically-motivated types of linear transformations, including rotations and projections, and compute their standard matrices.

Please leave a comment below if you have any questions, comments, or corrections.

Corrections:
- At 04:29, the vectors on both the left- and right-hand-sides of the figure are labelled e_1 and e_2. On the right they should be D(e_1) and D(e_2).

Timestamps:
00:00 - Introduction, identity and zero
02:10 - Diagonal transformations
05:02 - Projections
13:49 - Projection example
17:35 - Rotations
23:38 - Rotation example

[ephemeronchimera]

Let me just first say, you are a GODSEND! I cannot believe how well you explain the concepts and the way you relate everything geometrically truly aids in the learning and understanding process. Again, I cannot thank you enough for what you do. I am teaching myself the entire undergraduate curriculum for mathematics and just got done teaching myself Calculus 1-3 and am now tackling linear algebra before moving on to differential equations. I finally feel as though I am making progress, much more so than when I started studying the subject using Howard Anton's textbook. THANK YOU THANK YOU THANK YOU!!! You have truly been blessed with a gift for teaching what can be a complex subject matter in a truly understandable and engaging way that facilitates the learning process and makes for a deep and intuitive understanding of the subject matter.

[rd-tkjs]

Really understood the angle transformations for the first time, thanks !

[Klonedrekt]

Thanks for these lectures! I was wondering if there might be a mistake in the book on page 41, at the bottom: "these linear transformations are the ones for which there exist scalars c_1, c_2, ..., c_n ∈ ℝ^n". Should this not be "ℝ" without the ^n?

[PerfectGuyHere]

i think there is a mistake at 20:51. You have a column 2x1 vector(v1, v2) which you are multiplying by a square matrix 2x2 which should not be possible. According to the rule the column of matrix A and row of matrix B should be same to multiply. here they are different (1 and 2)