Jun 13, 2016 · Is a diagonal matrix with "$12$"s along the diagonal an identity matrix? Hot Network Questions If the death penalty is wrong because "what if the convicted was innocent", then isn't any punishment wrong?

Then $\|\cdot\|$ is a matrix norm with $\|I\| = \pi$. $\textbf{Edit:}$ If you are including the submultiplicativeness in the definition of your matrix norm (The definition of a matrix norm does not need to include the submultiplicative property), again pick your now favorite submultiplicative matrix norm $|\cdot|$ with $|I| = 1$.

$\begingroup$ Any vector subject to the identity matrix will give you the same vector back. That is the property of the identity matrix. But in light of eigenvectors and eigenvalues, this also matches the situation for eigenvalue =1 $\endgroup$ –

Jan 6, 2017 · (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; ...

May 16, 2018 · So it is possible for an identity matrix to be a standard matrix, but it's not always the case. Share. Cite.

All the powers of the identity matrix are equal to the identity matrix, so $\displaystyle I_n^k = I_n$.

Multiplication by identity matrix. 0. How unique is the orthogonal diagonalization of a real symmetric ...

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$\begingroup$ @Berci No, singular values are always non-negative, and the matrix need not be square/the operator need not be an endomorphism. And if it is an endomorphism, you generally consider two different orthonormal bases for the singular value decomposition. $\endgroup$

Oct 8, 2020 · In a non-Euclidean manifold, its components won't be those of an identity matrix even in Cartesian coordinates, because its eigenvalues will be of mixed sign. $\endgroup$ – J.G. Commented Oct 9, 2020 at 10:41