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 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 ...
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 that symbolize
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 orthogonal mean...
orthogonality - What does it mean when two functions are "orthogonal ...
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 terminology is unfortunate, but it is what it is.
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 corresponding to distinct eigenvalues are always orthogonal. If the eigenvalues are not distinct, an orthogonal basis for this eigenspace can be chosen using Gram-Schmidt.
I know a square matrix is called orthogonal if its rows (and columns) are pairwise orthonormal But is there a deeper reason for this, or is it only an historical reason? I find it is very confusin...
Then the integral for the inner product is akin to the summation in finite dimensional vector spaces. Then one could seek the analogy between expansion of a function as series (sum) of orthogonal functions with expansion of a vector in terms of orthogonal vectors in finite dimensional case.