Orthogonal Transformations and Matrices
... Solution note: Say A is orthogonal. Then the map TA is orthogonal. Hence its inverse is orthogonal, and so the matrix of the inverse, which is A−1 is orthogonal. By the previous problem, we know also that A−1 = AT is orthogonal. So since the columns of AT are orthonormal, which means the rows of A a ...
... Solution note: Say A is orthogonal. Then the map TA is orthogonal. Hence its inverse is orthogonal, and so the matrix of the inverse, which is A−1 is orthogonal. By the previous problem, we know also that A−1 = AT is orthogonal. So since the columns of AT are orthonormal, which means the rows of A a ...
Generalized Eigenvectors
... The second method of computing the generalized eigenvectors of degree two is a special case of the following more general result. Proposition 2. v is a generalized eigenvector of degree m if and only if (A - I)kv is a generalized eigenvector of degree m – k for k = 1, 2, …, m - 1. In particular, v ...
... The second method of computing the generalized eigenvectors of degree two is a special case of the following more general result. Proposition 2. v is a generalized eigenvector of degree m if and only if (A - I)kv is a generalized eigenvector of degree m – k for k = 1, 2, …, m - 1. In particular, v ...
