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Someone needs to get this man more recognition. He is a god

Great Videos! They have helped me out tremendously with computer graphics!

I respect you and your work. You've helped me a lot.

Awesome!

I think for students the matrix-multiplication will be easier to follow if you write it so that one is at the left and one above the place where the resulting matrix is written down. Apart from that i really like the way you teach these concepts.

bravo

We need quaternions! (for graphics programming :) )

If you multiply the rotation matrix by the basis vector in column vector form you will obtain the transformed basis vectors in the opposite order, why not write the rotation matrix components in row vector instead of column vector form (i.e. the transpose of what you wrote)?

And if we are in the Complex variables??? Still the Rotation Matrix has no eigenvalues for z not equal to nπ?

@MathTheBeautiful

6 жыл бұрын

Complex numbers change everything usually.

I am just NOT getting how my book, you, the internet in general, etc. derived the weird Trig matrix. How the heck is it [-sin, cos] on the right column? break it down like I'm an Algebra 1 student in 8th grade, pleeease.

@MathTheBeautiful

8 жыл бұрын

+chrisgosselin92 Well, let's try to get to the bottom of it. First, tell me what happens to the vector [ 1 0 ] under the rotation (i.e. what's the resulting vector)?

@chrisgosselin92

8 жыл бұрын

+MathTheBeautiful it moves to quadrant II of a Cartesian plane. The resulting values are (-x,y). For the vector [0 1] it moves into quadrant I and gives positive values for x and y. Is all of that right so far?

@MathTheBeautiful

8 жыл бұрын

+chrisgosselin92 No, you rotated (x,y) by 90 degrees. The task was to rotate (1,0) by angle theta

@chrisgosselin92

8 жыл бұрын

+MathTheBeautiful If I rotate the vector [1 0] by theta, it should go to quadrant I, and for vector [0 1] it would go to quadrant II, right? I think I mixed up the vectors the first time around.

@MathTheBeautiful

8 жыл бұрын

+chrisgosselin92 That's correct, but we're looking for the *specific components* of the image of the vector (1,0) under the rotation by the angle theta.