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Trace of square of a rank-$1$ Hermitian matrix ${\bf A} = {\bf a}{\bf a}^H$

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#linear-algebra #matrices #symmetric-matrices #matrix-analysis #rank-1-matrices
57
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Unitary matrix of polar decomposition

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#linear-algebra #matrices #matrix-decomposition #unitary-matrices #matrix-analysis
48
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Derivatives of Matrix Functions of Different Dimensions

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#linear-algebra #derivatives #matrix-calculus #matrix-analysis
136
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Dimension of the manifold of symmetric rank $r$ $n\times n$ matrices

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#differential-geometry #differential-topology #non-convex-optimization #matrix-analysis
94
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The spectral radius analysis

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#linear-algebra #numerical-linear-algebra #matrix-decomposition #matrix-analysis
36
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Why limit of a matrix's power exits will implies this?

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#linear-algebra #matrix-analysis
34
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vector but not matrix norm

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#normed-spaces #matrix-analysis
46
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Finding eigenvalues of the sum of two matrices.

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#linear-algebra #matrices #eigenvalues-eigenvectors #numerical-linear-algebra #matrix-analysis
66
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What is the second derivative of the spectral norm of a symmetric matrix?

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#matrices #hessian-matrix #matrix-norms #matrix-analysis #spectral-norm
60
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Algorithms to reduce matrix bandwidth

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#linear-algebra #algorithms #numerical-linear-algebra #matrix-analysis
42
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Backward error of solving $Ax=b$ with perturbed matrix $A$

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#analysis #numerical-methods #matrix-analysis
26
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Eigendecomposition of a block matrix of the form $\begin{pmatrix} A_{11} & A_{12} \\ A_{12}^T & 0 \end{pmatrix}$

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#linear-algebra #matrices #eigenvalues-eigenvectors #matrix-analysis
69
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Relating two seemingly different definitions of Riemannian metric.

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#differential-geometry #riemannian-geometry #definition #positive-definite #matrix-analysis
86
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Matrix inequality involving square root and positive matrices

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#matrices #matrix-calculus #positive-semidefinite #matrix-analysis
55
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Relations between row and columns of orthogonal matrix

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#linear-algebra #matrices #orthogonal-matrices #matrix-analysis

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