Sets of vectors are orthogonal or orthonormal. There is no such thing as an orthonormal matrix. An orthogonal matrix is a square matrix whose columns (or rows) form an orthonormal basis. …

41 I recently took linear algebra course, all that I learned about orthogonal matrix is that Q transposed is Q inverse, and therefore it has a nice computational property. Recently, to my …

Oct 7, 2022 · I see, thanks, so basically, an orthogonal matrix is one that ensures that the modulus of the magnitude of the basis vectors obtained is always 1, right?

The eigenvalues of an orthogonal matrix needs to have modulus one. If the eigenvalues happen to be real, then they are forced to be $\pm 1$. Otherwise though, they are free to lie anywhere …

The statement is imprecise: eigenvectors corresponding to distinct eigenvalues of a symmetric matrix must be orthogonal to each other. Eigenvectors corresponding to the same eigenvalue …

A matrix V V with mutually orthogonal columns is called orthogonal because it maps each of the standard orthogonal coordinate directions to a new set of mutually orthogonal coordinate …

May 8, 2012 · 81 In general, for any matrix, the eigenvectors are NOT always orthogonal. But for a special type of matrix, symmetric matrix, the eigenvalues are always real and eigenvectors …

Sep 27, 2013 · Orthogonal matrices are invertible square matrices, so their singular values are their eigenvalues. Their eigenvalues are complex numbers whose norm (i.e. absolute value) is …

Jun 17, 2021 · I had the following questions in my mind next: Are all elements of an orthogonal matrix real? Why can't they be complex? Can a complex matrix be orthogonal? Any productive …

The original question was asking about a matrix H and a matrix A, so presumably we are talking about the operator norm. The selected answer doesn't parse with the definitions of A and H …