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$A$ is normal if and only if $trace(A^\ast A)=\sum_{i=1}^n|\lambda_i|^2.$ where the $\lambda_i$ are the eigenvalues of $A$.

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#linear-algebra #matrices #matrix-decomposition
121
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Existence of matrix with $d_{ii} \in \{1,-1\}$ in QR decomposition

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#linear-algebra #matrices #numerical-methods #matrix-decomposition
30
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Is this a correct abreviation of the singular value decomposition algorithm?

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#linear-algebra #matrices #diagonalization #matrix-decomposition
269
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SVD rank k approximation: why is it sufficient to project the row vectors to approximate the matrix?

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#approximation #matrix-decomposition #matrix-rank #svd
247
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Complex matrix decomposition: Cholesky?

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#linear-algebra #matrices #matrix-decomposition
491
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Matrix decomposition minimizing infinity norm

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#matrices #optimization #normed-spaces #convex-optimization #matrix-decomposition
41
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Why did I write this equivalency involving an eigenvalue decomposition?

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#linear-algebra #eigenvalues-eigenvectors #matrix-equations #numerical-linear-algebra #matrix-decomposition
243
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Stuck in deriving decomposition of essential matrix(background in computer vision needed)

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#rotations #projective-geometry #matrix-decomposition #svd
126
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Characterize set of matrices that are orthogonal in two particular senses

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#linear-algebra #matrix-equations #orthogonality #matrix-decomposition #quantum-information
1k
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Eigenvalues of the addition of a symmetric matrix and the identity matrix

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#linear-algebra #matrices #eigenvalues-eigenvectors #matrix-decomposition #symmetric-matrices
86
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What's a pre-unitary (pre-u) matrix? And a pre-column-unitary (pre-c-u)?

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#matrices #matrix-equations #matrix-calculus #matrix-decomposition #matrix-rank
57
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Matrix row-echelon form issue

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#matrices #matrix-equations #matrix-calculus #matrix-decomposition #matrix-rank
2.4k
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Property of spectral norm

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#matrices #normed-spaces #matrix-decomposition
88
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About QR decomposition

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#matrices #matrix-equations #matrix-calculus #matrix-decomposition #matrix-rank
86
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How to solve L1 optimization of Low-Rank matrix?

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#linear-algebra #optimization #matrix-decomposition #regularization #nuclear-norm

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