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Prove that $T$ is invertible if and only if $0$ is not an eigenvalue of $T$

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#linear-algebra #eigenvalues-eigenvectors #determinant
127
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Question about eigenvalue and invertibility problem

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#linear-algebra #eigenvalues-eigenvectors #linear-transformations #determinant
855
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Spectral Norm of block diagonal matrix

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#eigenvalues-eigenvectors #diagonalization #svd #spectral-norm
103
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A linear function involving the global optimum of the Rayleigh quotient

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#real-analysis #optimization #eigenvalues-eigenvectors #convex-analysis #convex-optimization
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How to prove the largest eigenvalue of a matrix is smaller or equal to the max of absolute sum of rows?

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#linear-algebra #matrices #eigenvalues-eigenvectors
398
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If $A,B$ are diagonalisable, does $AB$ diagonalisable imply $BA$ diagonalisable?

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#linear-algebra #eigenvalues-eigenvectors #spectral-theory #diagonalization #characteristic-polynomial
95
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Eigenvalue of sum of two specific matrices

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#linear-algebra #eigenvalues-eigenvectors #spectral-theory
767
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Eigenvalues of $5 \times 5$ matrix with real entries from given condition

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#linear-algebra #eigenvalues-eigenvectors #characteristic-polynomial
151
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How will matrix $A^n$ affect the original eigenvector and eigenvalue?

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#linear-algebra #matrices #eigenvalues-eigenvectors
37
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bounds on matrix power

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#linear-algebra #matrices #eigenvalues-eigenvectors #uniform-convergence
1k
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Prove that a non-zero matrix satisfying $A^N = \textbf0$ for some $N$ cannot be diagonalized.

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#linear-algebra #matrices #eigenvalues-eigenvectors #diagonalization #nilpotence
35
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Properties of a Matrix that diagonalizes another matrix

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#matrices #eigenvalues-eigenvectors #diagonalization
553
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Correct way to represent eigenvalue spectra from varying eigendecomposition techniques (SVD, etc)?

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#eigenvalues-eigenvectors #svd #eigenfunctions
63
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Why is the following matrix product inequality true?

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#linear-algebra #matrices #inequality #eigenvalues-eigenvectors #upper-lower-bounds
134
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Eigenvalues of tridiagonal matrices with repeating/cyclic entries

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#matrices #eigenvalues-eigenvectors #physics

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