# Tagged Questions

For any topic related to matrices. This includes: systems of linear equations, eigenvalues and eigenvectors (diagonalization, triangularization), determinant, trace, characteristic polynomial, adjugate, transpose, Jordan normal form, matrix algorithms (e.g. LU, Gauss elimination, SVD, QR), ...

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### Inverse of a Matrix(shortcut and tricks)

Can someone tell me if there is any shortcut or trick of finding the inverse of a matrix and not by elementary operations? Also is it possible to judge an inverse of a matrix by judging the options ...
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### A question on Involuntary matrices [closed]

If A is a square matrix such that $A^2= I, then A^{-1}$is equal to what? (where I is the identity matrix)
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### Proof for functions of matrix [closed]

Let $A \in \text{Mat} (n,n,\mathbb{C})$. Let $I$ be a subset of $\mathbb{R}$ or $\mathbb{C}$. Further, let $f:I\to\mathbb{C}$ and $g:I\to\mathbb{C}$ be two functions for which $f(A)$ and $g(A)$ are ...
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### How to find a unique solution, infinite solution and no solution for this matrix. [closed]

The question on my page is For what value(s) of k does the system have, no solutions, a unique solution, and infinitely many solutions? All help is appreciated! Thanks in advance
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### Matrices over integer fields to solve complex polynomials.

Inspired by the fruitful answer to this question regarding numerically solving polynomial equations in terms of simpler fields (in that case representing real numbers as fractions of integers), I ...
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### Notation of a function that Maps two sets into a Matrix

Given two sets $P, V$ a function $f(t)$ takes any element that belongs to $P$ or $V$ e.g. $t \in P \cup V$ returns a matrix of $2$ columns and $K$ rows. What is the proper notation to express ...
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### prove that the product of a vector $\vec a$ and the transpose of a vector $\vec b$ is a $n \times n$ matrix with rank $1$

I need your help in solving this question. Given two vectors $\vec a$ and$\vec b$, prove that: The product of a vector $\vec a$ and the transpose of a vector $\vec b$ is a $n \times n$ ...
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### We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$

Problem: We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of elements in each row is zero. Prove that $\det(AA^T)=nk^2$, where $k\in \mathbb Z$. What have I considered so far: First ...
We have diagonal matrices $A = \mbox{diag} (\lambda_1, \ldots, \lambda_n)$ for which matrix exponential has simple form $e^A = \mbox{diag} (e^{\lambda_1}, \ldots, e^{\lambda_n})$, and it can be ...