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How to show that $det(AB-xI)=det(BA-xI)$ ,for any $x\in \mathbb F$.

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#matrices #eigenvalues-eigenvectors #linear-transformations #matrix-equations #characteristic-polynomial
140
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characteristic polynomial of block matrix

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#polynomials #minimal-polynomials #block-matrices #characteristic-polynomial
203
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How to prove that if $A$ is a square matrix on $\mathbb{R}$, $A$ is nilpotent, then trace($A$)=0

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#linear-algebra #eigenvalues-eigenvectors #determinant #trace #characteristic-polynomial
126
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Confusion about characteristic polynomial of AB and BA

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#linear-algebra #characteristic-polynomial
229
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How to get the characteristic polynomial of this matrix?

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#matrices #determinant #trace #characteristic-polynomial
177
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minimal polynomial, characteristic polynomial proof

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#linear-algebra #matrices #minimal-polynomials #characteristic-polynomial
394
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T(A) = A transpose

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#eigenvalues-eigenvectors #characteristic-polynomial
152
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Matrix and it's Transpose have the same eigenvalues?

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#matrices #eigenvalues-eigenvectors #characteristic-polynomial
60
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Finding characteristic polynomial

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#linear-algebra #matrices #polynomials #characteristic-polynomial
1.5k
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A and its transpose have the same minimal polynomial

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#linear-algebra #matrices #eigenvalues-eigenvectors #minimal-polynomials #characteristic-polynomial
60
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Find characteristic polynomial of $T^{-1}$

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#linear-algebra #linear-transformations #characteristic-polynomial
45
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finding the characteristic polynomial of symmetric matrix

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#determinant #symmetric-matrices #characteristic-polynomial
53
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How to find characteristic polynomial of a matrix $A$ such that $A=A^n$ for some $n\geq 2$?

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#linear-algebra #matrices #minimal-polynomials #characteristic-polynomial
41
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find all the matrices (which are not similiar) which fulfill this formula

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#jordan-normal-form #minimal-polynomials #characteristic-polynomial #cayley-hamilton #similar-matrices
127
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Alll the matrices $A\in M_{7x7}\left(\mathbb{C}\right)$, with characteristic polynomial is: $\left(x-1\right)^3\left(x-2\right)^4$, ...

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#matrices #jordan-normal-form #minimal-polynomials #characteristic-polynomial #cayley-hamilton

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