Matrix rotation explained with memes

[0 −1; 1 0] today [0 −1; 1 0][1; 3] = [?; ?] wait each by (0)(1) + (−1)(3) −3 1 (0, 1) (−1, 0) just gooooooo

A fast-paced educational comedy video explains how the matrix [0 −1; 1 0] multiplies the vector (1, 3), transforming it into (−3, 1) and rotating it 90 degrees anticlockwise. The lesson is intercut with increasingly confused and amazed reaction clips, turning straightforward linear algebra into an absurd dramatic reveal. The ending celebrates identifying the matrix’s transformed basis vectors. EN: A fast-paced educational comedy video explains how the matrix [0 −1; 1 0] multiplies the vector (1, 3), transforming it into (−3, 1) and rotating it 90 degrees anticlockwise. The lesson is intercut with increasingly confused and amazed reaction clips, turning straightforward linear algebra into an absurd dramatic reveal. The ending celebrates identifying the matrix’s transformed basis vectors.

Today I'm going to teach you about the matrix and not the one that tried to attack me. Is that a matrix? Correct. This one has two rows and two columns, right Andrew? Yeah, that's correct. Now listen, if we multiply a matrix by a vector, this will transform the vector. Wait, hold up, that's not a vector. A vector's like something times i plus something times j. It's just another way of writing vectors, bruv. This one would be one i plus three j, so as an arrow, it'd look like this. Oh, how'd you do the multiplication? Just multiply each row of the matrix by the vector column. Whoa, what do you mean by that? Well, hold on a second. Yeah, how are you going to times a row by a column? You just times the first two numbers in the row and column, then times the second two numbers and add everything together. The first matrix row multiplied by the vector column gives us the number that goes here. And then the second matrix row multiplied by the vector column gets us this bottom number. So by multiplying the matrix by our original vector 1, 3, we've transformed it into this new vector minus 3, 1. Oh, so this matrix turns vectors anti-clockwise? A perfect 90 degree rotation. Is there a way to know what transformation the matrix is going to do just by looking at it? Yeah, so this red and green arrow are our basis vectors, right? With coordinates 1, 0, and 0, 1. Now watch me multiply the matrix by each one and transform them. So that's the first one done. Don't stop cooking. There's the second one done. So any vector we transform is just going to follow the basis vectors, right? Now look at the first column of the matrix. Notice how that's where the tip of the red basis vector ends up. And the second column tells us where the tip of the green basis vector ends up.

• @antichirst / 18925 2025-02-13