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Does every polynomial with a Perron root have a primitive matrix representation?

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#linear-algebra #matrices #polynomials #companion-matrices #similar-matrices
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Modulus of eigenvalues of a companion matrix

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#matrices #eigenvalues-eigenvectors #companion-matrices
837
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Eigenvectors of companion matrix

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#linear-algebra #matrices #eigenvalues-eigenvectors #companion-matrices
287
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Finding the inverse of $A$

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#linear-algebra #matrices #inverse #companion-matrices
417
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When are almost block companion matrices which yield a given characteristic polynomial connected?

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#linear-algebra #general-topology #polynomials #connectedness #companion-matrices
664
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Explicit formula of exponential of companion matrix

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#linear-algebra #matrices #matrix-exponential #companion-matrices
552
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Solving differential equations given a companion matrix?

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#linear-algebra #matrices #ordinary-differential-equations #companion-matrices
243
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Is the cyclic vector for companion matrix independent of the specific companion matrix under consideration?

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#linear-algebra #matrices #cyclic-decomposition #companion-matrices
70
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Companion matrix, polynomial

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#matrices #companion-matrices
402
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Companion matrix for $(x^2+1)^2$

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#linear-algebra #matrices #polynomials #companion-matrices
837
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How to compute the characteristic polynomial of a companion matrix to a polynomial with matrix-valued coefficients?

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#linear-algebra #matrices #block-matrices #characteristic-polynomial #companion-matrices
135
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Smith Normal Form of a companion matrix of monic polynomial

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#linear-algebra #matrices #polynomials #smith-normal-form #companion-matrices
38
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Characteristic polynomial of $r \times r$ companion matrix

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#linear-algebra #matrices #finite-fields #cyclotomic-polynomials #companion-matrices
45
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Counting the powers of a companion matrix that possess nonzero leading principal minors

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#linear-algebra #matrices #polynomials #finite-fields #companion-matrices
467
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Show the matrix commutes with companion matrix is a polynomial

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#linear-algebra #matrices #minimal-polynomials #companion-matrices

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