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$A,B\in M_n(\mathbb{R})$ ($n\geq 2$) are such that $A^2=-I_n$ and $AB=BA$. Can we infer that $\det{B}\geq0$?

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#linear-algebra #matrices #eigenvalues-eigenvectors #determinant #characteristic-polynomial
84
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Classifying Matrices

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#linear-algebra #minimal-polynomials #characteristic-polynomial
20
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Spectrum of a strongly regular graph with a vertex deleted

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#algebraic-graph-theory #characteristic-polynomial
98
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What are the eigenvalues of a particular type of block partitioned matrix

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#linear-algebra #matrices #eigenvalues-eigenvectors #block-matrices #characteristic-polynomial
45
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Confusion about the primary decomposition theorem in linear algebra

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#linear-algebra #jordan-normal-form #minimal-polynomials #characteristic-polynomial #primary-decomposition
69
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A $4\times 4$ matrix counterexample.

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#linear-algebra #abstract-algebra #jordan-normal-form #minimal-polynomials #characteristic-polynomial
106
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Does similarity of matrices preserve sum of principal minors?

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#linear-algebra #matrices #trace #characteristic-polynomial #similar-matrices
178
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Determine the entries $x$ and $y$ in a matrix so that its only eigenvalue is $1$.

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#linear-algebra #matrices #eigenvalues-eigenvectors #determinant #characteristic-polynomial
31
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Simplifying eigenvalue calculation where only one non-zero element is shared by a row and column.

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#matrices #eigenvalues-eigenvectors #determinant #block-matrices #characteristic-polynomial
47
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Finding characteristic polynomial of a square matrix and how to proving that matrix is diagonalizable

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#linear-algebra #matrices #diagonalization #characteristic-polynomial
38
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Faster way to find the eigenvalues of a 4x4 real matrix?

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#linear-algebra #matrices #eigenvalues-eigenvectors #determinant #characteristic-polynomial
1k
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Finding the minimal polynomial from characteristic equation

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#matrices #notation #minimal-polynomials #characteristic-polynomial
1.5k
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Characteristic polynomial of a tridiagonal matrix

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#linear-algebra #matrices #eigenvalues-eigenvectors #characteristic-polynomial #tridiagonal-matrices
4k
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Eigenvalues of a companion matrix

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#linear-algebra #matrices #eigenvalues-eigenvectors #characteristic-polynomial #companion-matrices
197
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Diagonalizing a particular $3\times3$-matrix.

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#linear-algebra #matrices #algebra-precalculus #diagonalization #characteristic-polynomial

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