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Eigenvectors exclusively from the standard basis

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#linear-algebra #matrices #eigenvalues-eigenvectors
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How to determine the characteristic polynomial of the $4\times4$ real matrix of ones?

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#linear-algebra #matrices #eigenvalues-eigenvectors #determinant #characteristic-polynomial
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Questions about a proof for the Min-Max-Theorem for compact operators

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#functional-analysis #eigenvalues-eigenvectors
50
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Equivalent property of a positiv definite operator

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#functional-analysis #eigenvalues-eigenvectors #hilbert-spaces
110
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Matrix $A\in \mathbb{R}^{4\times4}$ has eigenvectors $\bf{u_1,u_2,u_3,u_4}$ satisfying $\bf{Au_1=5u_1,Au_2=9u_2}$ & $\bf{Au_3=20u_3}$. Find $A\bf{w}$.

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#linear-algebra #matrices #eigenvalues-eigenvectors #diagonalization
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Determinant of Block Tridiagonal Matrix

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#linear-algebra #matrices #eigenvalues-eigenvectors #recursion #block-matrices
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Can real non-symmetric matrices have real eigenvalues?

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#linear-algebra #matrices #eigenvalues-eigenvectors
216
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The matrix $f(A)$ has the eigenvalues $f(\lambda_k)$

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#linear-algebra #matrices #polynomials #eigenvalues-eigenvectors
402
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Constrained eigenvalue problem

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#linear-algebra #eigenvalues-eigenvectors #constraints
240
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Analyticity of eigenvalues: results from Katō and real-analytic forms

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#real-analysis #eigenvalues-eigenvectors
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Matrix transformations, Eigenvectors and Eigenvalues

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#matrices #eigenvalues-eigenvectors #linear-transformations #matrix-equations
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Spectrum of a matrix after applying an element-wise function (e.g. elementwise log)

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#eigenvalues-eigenvectors #upper-lower-bounds
31
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Why is it necessary to say “ λ 1 is simple” to conclude “A/λ1” has spectral radius 1?

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#eigenvalues-eigenvectors
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explicit description of eigenvector of a rotation

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#linear-algebra #abstract-algebra #matrices #eigenvalues-eigenvectors #rotations
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relation between rank of power of a singular matrix with the algebraic multiplicity of zero

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#eigenvalues-eigenvectors #matrix-rank

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