So would it be fair to consider the orthonormal/vector relationship the "opposite" of a matrix/eigenvector relationship, where orthonormal matrices change direction without changing magnitude while a matrix with its eigenvectors changes magnitude without changing direction.
No. U is orthonormal, meaning that dotting each respective vector (which is equivalent to matrix multiplication of transpose) produces a value of 1, which is the equivalent to saying the length of the vectors in col{U} (or equivalently row{U}) is 1 (hence, normal/normalized).
I love the idea of using my past Calc 3 knowledge to linear algebra now, I hope we get into some applications
"when i said 4, i meant 3" had me dead ngl 😂😂
Glad you enjoy my humor!
@@paulcartie7095 love it ❤️
So would it be fair to consider the orthonormal/vector relationship the "opposite" of a matrix/eigenvector relationship, where orthonormal matrices change direction without changing magnitude while a matrix with its eigenvectors changes magnitude without changing direction.
This is a test to see if my reply is added to your comment.
This class makes me want to take abstract algebra even though unsure if could ever fit that in a schedule without going over 4 years for a bachelor’s…
It is interesting how the inverse of the orthogonal matrix it's transpose
in 22:50 , could that at any chance mean that U(t) = U(-1) ?
No. U is orthonormal, meaning that dotting each respective vector (which is equivalent to matrix multiplication of transpose) produces a value of 1, which is the equivalent to saying the length of the vectors in col{U} (or equivalently row{U}) is 1 (hence, normal/normalized).