# 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? ...
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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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Identify all possible eigenvalues of an $n \times n$ matrix $A$ that satisfies the matrix equation: $A-2 I=-A^{2}$. Justify your answer.a) Identify all possible eigenvalues of an $n \times n$ matrix $A$ that satisfies the matrix equation: $A-2 I=-A^{2}$. Justify your answer. b) M ...
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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
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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 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} ...
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The characteristic polynomial of a square matrix is the polynomial $p(\lambda)=\operatorname{det}(\lambda I-$ $A$ ).
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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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Let $Z$ be a complex square matrix whose self-adjoint part is positive definite, so $Z+Z^{*}$ is positive definite.
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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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Let $A$ and $B$ be $n \times n$ complex matrices that commute: $A B=B A$. If $\lambda$ is an eigenvalue of $A$, let $\mathcal{V}_{\lambda}$ be the subspace of all eigenvectors having this eigenvalue.Let $A$ and $B$ be $n \times n$ complex matrices that commute: $A B=B A$. If $\lambda$ is an eigenvalue of $A$, let $\mathcal{V}_{\lambda ... close 0 answers 72 views Let \(M$ be a $2 \times 2$ matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant $c$. Which (if any) any of the vectorsLet $M$ be a $2 \times 2$ matrix with the property that the sum of each of the rows and also the sum of each of the columns is the same constant \ ...
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0 answers 209 views
Let $A$ be a square matrix and $p(\lambda)$ any polynomial. If $\lambda$ is an eigenvalue of $A$, show that $p(\lambda)$ is an eigenvalue of the matrix $p(A)$ with the same eigenvector.Let $A$ be a square matrix and $p(\lambda)$ any polynomial. If $\lambda$ is an eigenvalue of $A$, show that $p(\lambda)$ is an eigenvalue of ...
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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\ ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 Let \(L$ be an $n \times n$ matrix with real entries and let $\lambda$ be an eigenvalue of $L$. In the following list, identify all the assertions that are correct.
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Let $L$ be an $n \times n$ matrix with real entries and let $\lambda$ be an eigenvalue of $L$. In the following list, identify all the assertions that are correct.Let $L$ be an $n \times n$ matrix with real entries and let $\lambda$ be an eigenvalue of $L$. In the following list, identify all the asserti ...
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0 answers 193 views
Let $A$ be an invertible matrix. If $\mathbf{V}$ is an eigenvector of $A$, show it is also an eigenvector of both $A^{2}$ and $A^{-2}$. What are the corresponding eigenvalues?Let $A$ be an invertible matrix. If $\mathbf{V}$ is an eigenvector of $A$, show it is also an eigenvector of both $A^{2}$ and $A^{-2}$. What ...
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Let $A$ be an $n \times n$ real self-adjoint matrix and $\mathbf{v}$ an eigenvector with eigenvalue $\lambda$. Let $W=\operatorname{span}\{\mathbf{v}\}$.
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Let $A$ be an $n \times n$ real self-adjoint matrix and $\mathbf{v}$ an eigenvector with eigenvalue $\lambda$. Let $W=\operatorname{span}\{\mathbf{v}\}$.Let $A$ be an $n \times n$ real self-adjoint matrix and $\mathbf{v}$ an eigenvector with eigenvalue $\lambda$. Let $W=\operatorname{span}\{\m ... close Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993 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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Let $A: \mathbb{R}^{n} \rightarrow \mathbb{R}^{n}$ be a self-adjoint map (so $A$ is represented by a symmetric matrix).
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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).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 ...
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