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Recent questions tagged self-adjoint


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When is a matrix \(M\) normal?
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When is a matrix \(M\) normal?When is a matrix \(M\) normal? ...
by Pieter Gold Status
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asked in Mathematics May 6
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Identify all possible eigenvalues of an \(n \times n\) matrix \(A\) that satisfies the matrix equation: \(A-2 I=-A^{2}\). Justify your answer.

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Show that \(p(\lambda)=\lambda^{n}+a_{n-1} \lambda^{n-1}+\cdots+a_{0}\) is the characteristic polynomial of the matrix
0 answers 160 views
Show that \(p(\lambda)=\lambda^{n}+a_{n-1} \lambda^{n-1}+\cdots+a_{0}\) is the characteristic polynomial of the matrixShow that \(p(\lambda)=\lambda^{n}+a_{n-1} \lambda^{n-1}+\cdots+a_{0}\) is the characteristic polynomial of the matrix \ A=\left(\begin{array}{ccccc} ...
by MathsGee Platinum
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asked in Mathematics Jan 21
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The characteristic polynomial of a square matrix is the polynomial \(p(\lambda)=\operatorname{det}(\lambda I-\) \(A\) ).
0 answers 169 views
The characteristic polynomial of a square matrix is the polynomial \(p(\lambda)=\operatorname{det}(\lambda I-\) \(A\) ).The characteristic polynomial of a square matrix is the polynomial \(p(\lambda)=\operatorname{det}(\lambda I-\) \(A\) ). a) If two square matrices ar ...
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asked in Mathematics Jan 21
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Let \(Z\) be a complex square matrix whose self-adjoint part is positive definite, so \(Z+Z^{*}\) is positive definite.
0 answers 200 views
Let \(Z\) be a complex square matrix whose self-adjoint part is positive definite, so \(Z+Z^{*}\) is positive definite.Let \(Z\) be a complex square matrix whose self-adjoint part is positive definite, so \(Z+Z^{}\) is positive definite. a) Show that the eigenvalues o ...
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asked in Mathematics Jan 21
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Let \(A \in M(n, \mathbb{F})\) have an eigenvalue \(\lambda\) with corresponding eigenvector \(v\). True or False
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Let \(A \in M(n, \mathbb{F})\) have an eigenvalue \(\lambda\) with corresponding eigenvector \(v\). True or FalseLet \(A \in M(n, \mathbb{F})\) have an eigenvalue \(\lambda\) with corresponding eigenvector \(v\). True or False a) \(-v\) is an eigenvector of \(-A\ ...
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asked in Mathematics Jan 21
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Show that both \(A^{*} A\) and \(A A^{*}\) are self-adjoint.
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Show that both \(A^{*} A\) and \(A A^{*}\) are self-adjoint.Let \(A\) be a real matrix, not necessarily square. a) Show that both \(A^{} A\) and \(A A^{}\) are self-adjoint. b) Show that both \(A^{} A\) and ...
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asked in Mathematics Jan 21
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Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}\) be a self-adjoint map (so \(A\) is represented by a symmetric matrix).
0 answers 193 views
Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}\) be a self-adjoint map (so \(A\) is represented by a symmetric matrix).Let \(A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}\) be a self-adjoint map (so \(A\) is represented by a symmetric matrix). Show that (image \(A)^{\pe ...
by MathsGee Platinum
(118,646 points)
asked in Mathematics Jan 21
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