# Questions tagged [matrices]

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate and adjoint, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), invariant factors, quadratic forms, etc. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

35,939 questions
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### Eigenvalues of an antihermitian matrix

I have to prove that every eigenvalue of an antihermitian matrix is in the form of $bi$ for some $b \in R$. I already know that if A is antihermitian , it is normal , thus we can diagonalise it ...
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### standard definition and notation for a truncated permutation

I am seeking the standard notations or the standard way to define a truncated uniform random permutation. Let $M$ be an $n \times n$ matrix where each row and each column contain a single 1 and all ...
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### Non-Negative Vs Positive Semi Definite

A matrix is PSD if $$\langle Ax, x\rangle \ge 0, \forall x \in H$$ Where, H is a hilbert space and A is a mapping $H \rightarrow H$. Is it the same as being Non-negative? I couldn't seem to find a ...
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### Inverse Matrix in Python

My understanding is that I can use Python to initialize my matrix and then apply an inverse function to find the solution.
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### complexity of QR decomposition .

Could anyone help me to find the complexity of QR decomposition of matrix $A \in C^{N \times P}$, where $P \leq N$. I am also willing to know the complexity of adding a matrix $A \in C^{N \times N}$ ...
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### When do matrices respect inequalities?

Suppose I have vectors $u, v \in \mathbb{R}^n$ such that $u \le v$, meaning that, component-wise, each element of $u$ is less than or equal to the corresponding component in $v$. I am curious about ...
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### Characterisation of Permutation Matrices

$\newcommand\mat{\mathbf}$A permutation matrix is a matrix whose columns are a permutation of the columns of the identity matrix $\mat I$. In other words, a permutation matrix is a matrix $\mat P$ ...
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### If A is a real non-singular square matrix, then there exists a real matrix $B$ such that $e^B$ $=$ $A^2$

If we consider the matrix exponential map on $M_n(\mathbb R)$, then what will be the image set of the exponential map? I have seen this. From there I can say that $exp(M_n(\mathbb C))=GL_n(\mathbb C)$...
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### Prove that if matrix $C = I - 2M$ and $M = M^2,$ then $C^3 = C.$

I'm faced with a problem for which I haven't been given a correction, so I expected you could tell me if I am right or not, and in the later case give me the appropriate answer. Let $M$ be an ...
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### Is it possible to convert world coordinate to screen coordinate without using matrices?

Out of curiosity, I'm wondering if it is possible to calculate screen coordinate from world coordinate without using matrices. To calculate the screen coordinate, I need Model-view(Camera, scale, ...
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### Question on the definition of an Inverse matrix [duplicate]

By definition, if $A$ is a $n \times n$ matrix, an inverse of $A$ is an $n \times n$ matrix $A^{-1}$ with the property that: $$A^{-1}A=\mathbb I_n \ \ \land \ \ AA^{-1}=\mathbb I_n \ \ \ \ (1)$$ ...
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### Estimation of eigenvalues for online convergence estimation

Given some matrix $A$ of the form: $$A \equiv \left(H^\mathrm{H}\Sigma H + \Lambda\right)$$ with $\Sigma$ and $\Lambda$ full-rank diagonal real matrices, and $H$ a large rank deficient not-...