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minimal and characteristic polynomial of this operator

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#linear-algebra #matrices #minimal-polynomials #characteristic-polynomial #companion-matrices
54
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Does the minimal polynomial and characteristic polynomial have same roots over F, for a linear operator on vectorspace V over the field F?

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#linear-algebra #vector-spaces #roots #minimal-polynomials #characteristic-polynomial
55
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The characteristic polynomial of this family of matrices

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#linear-algebra #matrices #determinant #characteristic-polynomial
142
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Eigenvalues after multiplication with permutation matrix.

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#linear-algebra #eigenvalues-eigenvectors #characteristic-polynomial #permutation-matrices
56
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Show that $\text{Tr} (A)=\sum_{i=1}^rm_i\lambda_i$

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#linear-algebra #eigenvalues-eigenvectors #characteristic-polynomial
65
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Prove or disprove if $m(x)=\prod_{j=1}^{s}(x-\lambda_{j}^{2})$ is the minimal polynomial of a linear map $T\circ T:V\to V$

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#linear-algebra #linear-transformations #minimal-polynomials #characteristic-polynomial
359
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Fundamentally, what's a characteristic polynomial?

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#characteristic-polynomial
60
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Find the dimension of the vector space V.

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#linear-algebra #matrices #eigenvalues-eigenvectors #characteristic-polynomial
285
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General analytical method for determining whether a system of ODEs exhibits damped oscillations?

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#ordinary-differential-equations #dynamical-systems #characteristic-polynomial
85
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Characteristic polynomial of A and -A (where A is a companion matrix)

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#characteristic-polynomial #companion-matrices
132
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Calculating eigenvalues of a matrix

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#linear-algebra #matrices #eigenvalues-eigenvectors #characteristic-polynomial
299
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To find minimal polynomial of a matrix

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#minimal-polynomials #characteristic-polynomial
123
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Characteristic polynomial of linear recurrences

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#linear-algebra #recurrence-relations #characteristic-polynomial
144
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Characteristic polynomial of the symmetric matrix

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#linear-algebra #eigenvalues-eigenvectors #characteristic-polynomial
745
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Can a matrix have no eigenvectors?

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#linear-algebra #matrices #eigenvalues-eigenvectors #characteristic-polynomial

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