2011年2月11日 · In debate(?), "orthogonal" to mean "not relevant" or "unrelated" also comes from the above meaning. If issues X and Y are "orthogonal", then X has no bearing on Y. If you …

2015年7月12日 · 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 …

2017年8月26日 · An orthogonal basis can be used to decompose something into independent components. For example, the Fourier transform decomposes a time domain function into …

2015年8月4日 · Two vectors are orthogonal if their inner product is zero. In other words $\langle u,v\rangle =0$. They are orthonormal if they are orthogonal, and additionally each vector has …

2023年7月30日 · 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 …

Generally, those matrices that are both orthogonal and have determinant $1$ are referred to as special orthogonal matrices or rotation matrices. If I read "orthonormal matrix" somewhere, I …

So, basically, orthogonal matrix is just a combination of one-dimensional reflectors and rotations written in appropriately chosen orthonormal basis (the coordinate system you're used to, but …

Also, orthogonal set and linearly independent set both generate the same subspace. (Is that right?) Then orthogonal $\rightarrow$ linearly independent but orthogonal $\nleftarrow$ …

The original question was asking about a matrix H and a matrix A, so presumably we are talking about the operator norm.

As far as I know orthogonality is a linear algebraic concept, where for a 2D or 3D case if the vectors are perpendicular we say they are orthogonal. Even it is OK for higher dimensions. But …