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Give an example of matrices such that $ 0 $ is an eigenvalue of $ AB $ but not of $ BA $.

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#linear-algebra #matrices #eigenvalues-eigenvectors
774
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Proving a matrix has non trivial solution

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#linear-algebra #matrices #determinant
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Proof: Show that $A^2=A$ is diagonalizable

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#linear-algebra #matrices #diagonalization #idempotents
118
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Inverse matrix inequality

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#matrices
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Eigenvalues of product of two symmetric positive semi-definite real matrices.

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#linear-algebra #matrices #eigenvalues-eigenvectors #positive-semidefinite
750
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Proof of subordinate matrix norm equality

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#matrices #normed-spaces
156
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Graph Symmetry and Schur's Lemma in Group Representation

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#matrices #graph-theory #representation-theory #symmetric-groups #symmetry
400
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Subset of matrix rows with half of column sums

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#combinatorics #matrices #linear-programming
48
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Complementary subspace of $W = v_1+v_2+v_3$

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#matrices #vector-spaces
222
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Show that if $\lim_{t\to\infty} \int_0^t \operatorname{tr}(A(s))ds=\infty$, then $x'(t) = A(t)x(t)$ has an unbounded solution.

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#matrices #ordinary-differential-equations
65
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Given eigenvectors and eigenvalues of a matrix $A$, how to find its inverse and the limit of $A^nv$?

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#linear-algebra #matrices #limits #eigenvalues-eigenvectors
82
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Does this property imply total unimodularity?

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#linear-algebra #matrices #total-unimodularity #unimodular-matrices
82
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What is the rank of $B$?

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#linear-algebra #matrices #determinant #matrix-rank #tridiagonal-matrices
1.2k
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Inverse of any identity matrix

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#matrices
81
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Prove that determinant involving angles of triangle is purely real

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#matrices #determinant

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