Feb 11, 2011 · I 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 …

Aug 26, 2017 · Orthogonal 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 …

Jul 12, 2015 · I 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 …

Aug 4, 2015 · I 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?

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. The …

May 8, 2012 · 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 corresponding to …

Mar 7, 2016 · If my reasoning is correct than, for any basis in a vector space there is an inner product such that the vectors of the basis are orthogonal. If we think at vectors as oriented segments (in pure …

Now find an orthonormal basis for each eigenspace; since the eigenspaces are mutually orthogonal, these vectors together give an orthonormal subset of $\mathbb {R}^n$. Finally, since symmetric …

Sep 29, 2019 · In this manner we end up with a description for an infinite family of orthogonal vectors, which hopefully makes it easy for you to convince yourself intuitively. In a more general vector space, …

Nov 4, 2015 · To 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.