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. …

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 …

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 …

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 …

The short answer for "why" is that Charles Hermite called such a matrix an "orthogonal matrix" in 1854 and the name has stuck.

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 …

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 …

May 2, 2015 · The term "orthogonal matrix" probably comes from the fact that such a transformation preserves orthogonality of vectors (but note that this property does not …

Apr 22, 2016 · 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 …