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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
121
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Let A be a complex $n \times n$ matrix with rank(A) = 1. Why is the minimal polynomial $x(x-Tr(A))$?

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#linear-algebra #matrix-rank #trace #minimal-polynomials #rank-1-matrices
57
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Characteristic polynomial of convex combination

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#linear-algebra #convex-analysis #numerical-linear-algebra #characteristic-polynomial #rank-1-matrices
63
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Why is $xx'$ singular but ${\Bbb E}[xx']$ not (necessarily)?

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#probability #matrices #expected-value #correlation #rank-1-matrices
60
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How to quickly tell this matrix is not rank 1?

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#linear-algebra #matrices #rank-1-matrices
22
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Verify Sherman–Morrison–Woodbury rank-one update inverse

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#linear-algebra #matrices #matrix-equations #rank-1-matrices
448
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Singularity of a conic combination of rank-$1$ matrices

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#linear-algebra #matrices #decision-problems #rank-1-matrices
844
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Given matrices $A$ and $B$, how can I find a scalar $s$ that makes $A + s B$ rank-$1$?

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#linear-algebra #matrices #matrix-rank #svd #rank-1-matrices
65
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How to get orthogonal rank-$1$ approximations?

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#matrices #orthogonality #matrix-rank #rank-1-matrices
2.2k
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Rank-$1$ matrices

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#linear-algebra #matrices #rank-1-matrices
76.9k
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A rank-one matrix is the product of two vectors

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#linear-algebra #matrices #vector-spaces #matrix-rank #rank-1-matrices
2.3k
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Some basic questions regarding rank-$1$ matrices

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#linear-algebra #matrices #eigenvalues-eigenvectors #matrix-rank #rank-1-matrices
513
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Is the product of a diagonal matrix and a rank-$1$ matrix still rank-$1$?

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#matrices #eigenvalues-eigenvectors #diagonalization #matrix-rank #rank-1-matrices
70
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quick factorization of rank-one matrices (generally, and of a particular form)

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#linear-algebra #matrices #numerical-linear-algebra #svd #rank-1-matrices
19.8k
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Rank of sum of rank-$1$ matrices

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#linear-algebra #matrices #matrix-rank #rank-1-matrices

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