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A quadratic matrix equation

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#linear-algebra #matrices #algebraic-geometry #matrix-equations
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How to solve matrix equation $AX + B = XC$?

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#linear-algebra #matrices #matrix-equations
237
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Determine linear combination of rank 1 matrices for a rank 2 matrix?

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#linear-algebra #matrix-equations #matrix-decomposition #matrix-rank
67
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How can I show that $A^{-} A=I_{n} \text { if and only if } \operatorname{rank}(A)=n$?

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#matrices #matrix-equations #matrix-rank
66
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Intersection of subspaces: $U_1 = Sp\{x^3+2x^2+3x+6, 4x^3-x^2+3x+6, 5x^3+x^2+6x+12\}$, $U_2 = Sp\{x^3-x^2+x+1,2x^3-x^2+4x+5\}.$

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#linear-algebra #matrices #matrix-equations #matrix-rank #homogeneous-equation
278
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Find the value of the determinant $M$ from the equation $M = 3A^2 + AB + B^2$

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#linear-algebra #matrices #determinant #matrix-equations
147
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Values of integer such that a matrix equality does hold

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#linear-algebra #matrices #matrix-equations #matrix-calculus
70
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Matrix inequality that follows from other inequality

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#linear-algebra #matrices #matrix-equations
126
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solve matrix equation $2AX-X^TA=B$

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#matrices #systems-of-equations #matrix-equations
81
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Finding the symmetric square roots of diagonal matrices

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#linear-algebra #matrices #matrix-equations #symmetric-matrices #block-matrices
230
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Proof of $(\mathrm{Df}(X))(H)=XH+HX$

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#linear-algebra #matrix-equations #matrix-calculus
164
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The matrix equation $L^* \rho L+ L \rho L^* = L^* L \rho + \rho L^* L$

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#linear-algebra #matrix-equations
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If X is a characteristic vector of matrix A , then kX is also a character vector of A corresponding to the same characteristic value

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#matrices #eigenvalues-eigenvectors #vectors #matrix-equations
238
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How can the Poisson equation be numerically solved when its matrix is ​ill-conditioned in nature?

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#linear-algebra #matrix-equations
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When does multiplication by an orthogonal matrix preserves the eigenvalues?

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#linear-algebra #eigenvalues-eigenvectors #matrix-equations #matrix-calculus #orthogonal-matrices

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