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Given $X, Y \in \Bbb C^{n \times n}$ and $XY+2YX=3I$, show $[X,Y]$ is nilpotent

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#linear-algebra #matrices #nilpotence #characteristic-polynomial
78
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Show that $Tr(A)$ is in the spectrum of $A+I$

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#eigenvalues-eigenvectors #irreducible-polynomials #minimal-polynomials #cyclotomic-polynomials #characteristic-polynomial
105
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Does an algebra automorphism of $M_n(R)$ preserves the characteristic polynomial?

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#linear-algebra #abstract-algebra #commutative-algebra #characteristic-polynomial
142
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Eigenvalues of two symmetric tridiagonal Toeplitz matrices

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#matrices #eigenvalues-eigenvectors #block-matrices #characteristic-polynomial #toeplitz-matrices
279
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Conjecture: Any two matrices of size $n×n$ with same characteristic and minimal polynomial are similar implies $n\le 3$.

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#linear-algebra #abstract-algebra #jordan-normal-form #characteristic-polynomial #similar-matrices
88
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Matrix that commutes with a given matrix

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#linear-algebra #matrices #minimal-polynomials #characteristic-polynomial
239
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Is the ideal generated by coefficients of characteristic polynomial of a matrix prime?

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#linear-algebra #matrices #commutative-algebra #maximal-and-prime-ideals #characteristic-polynomial
92
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Is there any visual relationship between a matrix and its characteristic polynomial?

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#linear-algebra #characteristic-polynomial
53
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How to find the characteristic equation of the following coupled time delayed system?

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#characteristic-polynomial #delay-differential-equations
38
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Find a minimal polynomial of some matrix given a minimal polynomial of another matrix.

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#linear-algebra #eigenvalues-eigenvectors #minimal-polynomials #characteristic-polynomial
76
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Question related to eigenvalues and characteristic polynomial

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#linear-algebra #matrices #eigenvalues-eigenvectors #characteristic-polynomial
46
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Prove that the following statements are equivalent.

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#matrices #eigenvalues-eigenvectors #nilpotence #characteristic-polynomial
83
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Given a polynomial $P(x)$, is it always possible to construct a matrix with characteristic polynomial $P$?

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#linear-algebra #matrices #characteristic-polynomial
48
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minimal polynomial of finite field

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#linear-algebra #prime-numbers #finite-fields #jordan-normal-form #characteristic-polynomial
59
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An $n\times n$ matrix, $n\ge 2$ with characteristic polynomial $x^{n-2}(x^2-1)$

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#matrices #matrix-equations #matrix-rank #characteristic-polynomial #cayley-hamilton

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