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Variational form of matrix

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#derivatives #matrix-calculus
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Continuity of a matrix valued function

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#matrices #continuity #matrix-calculus
191
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Prove that if the matrix $\begin{bmatrix}a & b\\b & c\end{bmatrix}$ is nonnegative definite, then it has a factorization $LL^{T}$

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#calculus #linear-algebra #matrices #matrix-calculus #matrix-decomposition
169
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$\lim_{k\to \infty} A^k v=0$ with dominant eigenvalue $1$ and generalized eigenvector

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#linear-algebra #limits #eigenvalues-eigenvectors #exponentiation #matrix-calculus
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Is it true: A real block diagonal matrix is diagonalizable if and only if each block is diagonalizable.

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#linear-algebra #matrices #matrix-calculus #matrix-decomposition
66
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Eigenvalues of Matrix Polynomials and transformations that leave them invariant

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#matrices #polynomials #eigenvalues-eigenvectors #matrix-calculus #spectral-theory
210
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Derivative of an elementwise function and a pesudoinverse

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#linear-algebra #matrix-calculus #pseudoinverse
130
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On the solution of one matrix differential equation

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#matrices #ordinary-differential-equations #matrix-equations #matrix-calculus
15.7k
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When can we say that $A^{\mathrm T} B = B^{\mathrm T} A$?

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#matrices #matrix-calculus #linear-regression #transpose
158
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Can a tensor of rank-2 be diagonalized by two different set of basis?

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#tensors #matrix-calculus #diagonalization #change-of-basis
233
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Derivative of squared Frobenius norm of linear combination of rank-$1$ matrices with respect to their weights

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#linear-algebra #matrices #multivariable-calculus #derivatives #matrix-calculus
4k
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Partial derivative of matrix product in neural network

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#calculus #linear-algebra #matrices #matrix-calculus #neural-networks
848
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Differentiating with respect to a vector transpose

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#matrix-calculus #regression #least-squares #linear-regression
105
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Matrix with distinct eigenvectors corresponding to eigenvalues.

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#matrices #eigenvalues-eigenvectors #matrix-calculus #matrix-decomposition
128
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Derivative of $\mathrm{tr}(X^\top A) A$

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#matrices #derivatives #matrix-calculus

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