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Definiteness of matrix given definiteness of principal submatrix

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#linear-algebra #matrices #eigenvalues-eigenvectors
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Eigenvalues of Left Shift + Right Shift in $l_2([0,\infty))$

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#functional-analysis #eigenvalues-eigenvectors #operator-theory #hilbert-spaces #spectral-theory
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Linear combination of eigenvectors corresponding to the same eigenvalue

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#linear-algebra #eigenvalues-eigenvectors
185
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Eigenvectors and Generalized Eigenvectors

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#linear-algebra #abstract-algebra #eigenvalues-eigenvectors #diagonalization
115
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Polynomial Matrix Eigenvalue problem. Conditions under which there are only two complex eigenvalues?

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#matrices #polynomials #eigenvalues-eigenvectors
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How to determine if a 3x3 matrix is diagonalizable?

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#matrices #eigenvalues-eigenvectors #diagonalization
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Prove that $T,S$ are simultaneously diagonalizable iff $TS=ST$.

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#linear-algebra #matrices #eigenvalues-eigenvectors #transformation
567
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How does pointwise multiplication of two matrices affect their eigenvectors?

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#linear-algebra #matrices #eigenvalues-eigenvectors
90
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Generalized Eigenvector Problem

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#linear-algebra #optimization #eigenvalues-eigenvectors
840
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If $T^k = Id$ for $k\ge 1$ then $T$ is diagonalizable

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#linear-algebra #matrices #eigenvalues-eigenvectors #diagonalization #jordan-normal-form
149
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Finding complex eigenvectors of $n \times n$ matrix, $n\geq 3$

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#linear-algebra #matrices #complex-numbers #eigenvalues-eigenvectors
181
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$p(x)$ divides the minimal polynomial iff $\exists v\ne 0: p(T)(v)=0$

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#linear-algebra #eigenvalues-eigenvectors #transformation #irreducible-polynomials
290
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Under what assumptions is it correct to say "a matrix is diagonalizable if and only if its eigenvalues are real"?

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#linear-algebra #matrices #eigenvalues-eigenvectors #diagonalization
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Eigenvalues of a nilpotent matrix can only be $0$

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#linear-algebra #matrices #eigenvalues-eigenvectors
111
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What is the linear space of Eigenvectors associated with a certain Eigenvalue?

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#linear-algebra #matrices #eigenvalues-eigenvectors #diagonalization

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