http://www.bing.com:80/search?q=Orthogonal+DiagonalizationSearch resultshttp://www.bing.com:80/s/a/rsslogo.gifhttp://www.bing.com:80/search?q=Orthogonal+DiagonalizationCopyright © 2026 Microsoft. All rights reserved. These XML results may not be used, reproduced or transmitted in any manner or for any purpose other than rendering Bing results within an RSS aggregator for your personal, non-commercial use. Any other use of these results requires express written permission from Microsoft Corporation. By accessing this web page or using these results in any manner whatsoever, you agree to be bound by the foregoing restrictions.https://math.stackexchange.com/questions/2406260/difference-between-perpendicular-orthogonal-and-normalOrthogonal is likely the more general term. For example I can define orthogonality for functions and then state that various sin () and cos () functions are orthogonal. An orthogonal basis can be used to decompose something into independent components. For example, the Fourier transform decomposes a time domain function into weights of sines and cosines. A triple in 3D space is a decomposition ...Thu, 02 Apr 2026 02:04:00 GMThttps://english.stackexchange.com/questions/12219/usage-of-the-word-orthogonal-outside-of-mathematicsI always found the use of orthogonal outside of mathematics to confuse conversation. You might imagine two orthogonal lines or topics intersecting perfecting and deriving meaning from that symbolizeFri, 03 Apr 2026 03:07:00 GMThttps://math.stackexchange.com/questions/1358485/what-does-it-mean-when-two-functions-are-orthogonal-why-is-it-importantI have often come across the concept of orthogonality and orthogonal functions e.g in fourier series the basis functions are cos and sine, and they are orthogonal. For vectors being orthogonal mean...Sat, 04 Apr 2026 05:58:00 GMThttps://math.stackexchange.com/questions/1383725/what-is-the-difference-between-orthogonal-and-orthonormal-in-terms-of-vectors-anI am beginner to linear algebra. I want to know detailed explanation of what is the difference between these two and geometrically how these two are interpreted?Tue, 31 Mar 2026 19:46:00 GMThttps://math.stackexchange.com/questions/4731161/orthogonal-vs-orthonormal-matrices-what-are-simplest-possible-definitions-andSets 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. The terminology is unfortunate, but it is what it is.Thu, 02 Apr 2026 06:29:00 GMThttps://math.stackexchange.com/questions/142645/are-all-eigenvectors-of-any-matrix-always-orthogonalIn 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 corresponding to distinct eigenvalues are always orthogonal.Fri, 03 Apr 2026 01:55:00 GMThttps://math.stackexchange.com/questions/1201002/how-to-find-an-orthogonal-vector-given-two-vectorsOk. So taking the cross product gives me orthogonal vector in $\mathbb {R}^3$. And how to approach the same question in $\mathbb {R}^2$ for example...I mean with two vectors each having two componetns?Fri, 03 Apr 2026 09:05:00 GMThttps://math.stackexchange.com/questions/653133/eigenvalues-in-orthogonal-matricesTwo is false. The determinant is $\pm 1$, not the eigenvalues in general. Take a rotation matrix for example.Wed, 25 Mar 2026 16:32:00 GMThttps://math.stackexchange.com/questions/1511435/what-does-it-mean-for-two-functions-to-be-orthogonalTo check whether two functions are orthogonal, you simply take their inner product in $\mathbb {R}^n$. That is, you multiply the functions on the subintervals and then sum the products.Wed, 01 Apr 2026 18:33:00 GMThttps://math.stackexchange.com/questions/1261994/what-does-it-mean-for-two-matrices-to-be-orthogonalThe term "orthogonal matrix" probably comes from the fact that such a transformation preserves orthogonality of vectors (but note that this property does not completely define the orthogonal transformations; you additionally need that the length is not changed either; that is, an orthonormal basis is mapped to another orthonormal basis).Mon, 30 Mar 2026 01:24:00 GMT