Linear Transformations

MIT 18.06SC Linear Algebra, Fall 2011
Instructor: Nikola Kamburov

A teaching assistant works through a problem on linear transformations.

License: Creative Commons BY-NC-SA

[NisargJain]

My answer to the T matrix when v is taken as input basis and w as output basis is:

[ 1 0 0 0 ]
[ 0 0 0 1 ]
[ 0 1/2 1/2 0 ]
[ 0 -1/2 1/2 0 ]

[erikumble]

If you let v1, ..., v4 be the input basis, and w1, ..., w4 be the output basis, I think the transformation is described by the matrix ([1 0 0 0], [0 0 0 1], [0 1/2 1/2 0], [0 -1/2 1/2 0]). In the video, the input basis = output basis, but in the lecture, Professor Strang mentioned the possibility of a separate basis for input as output.

[dlseller]

Part 3 is vague because it does not say which basis to assume.
If we assume the standard basis we get eigenvectors v1, v4 with eigenvalues 1.

[sudharshantr]

does eigen vectors have a meaning when the input and output basis are different?

[go_all_in_]

Why is the inverse of T equal to T? I think that [T(A)]^-1 = T(A^-1), since (A^-1)^t = (A^t)-1. What am I doing wrong?

[juancarlospineros]

Why do we end up with a 4 by 4 matrix in the transformations of the 2 by 2 matrices?

[dfaburst]

I can feel this guy's nervousness thru the screen, almost distracting sorry