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Sets of vectors are orthogonal or orthonormal If i generate a random matrix a with every element sampled from a uniform [0, 1) distribution, and then use the gram schmidt procedure to get an orthogonal matrix q There is no such thing as an orthonormal matrix
An orthogonal matrix is a square matrix whose columns (or rows) form an orthonormal basis Absolute value) is $1$, or. 39 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
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 of a. 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 on.
Thus the first statement is just diagonalization while the one with $pdp^t$ is actually the exact same statement as the first one, but in the. It is important to note that the orthogonal matrix can have complex eigenvalues. 5 a particular case when orthogonal matrices commute Orthogonal matrices are used in geometric operations as rotation matrices and therefore if the rotation axes (invariant directions) of the two.
The term orthogonal matrix probably comes from the fact that such a transformation preserves orthogonality of vectors (but note that this property does not.
Orthogonal matrices are invertible square matrices, so their singular values are their eigenvalues Their eigenvalues are complex numbers whose norm (i.e
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