# Tagged Questions

Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically ...

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### Perspective correction from 3 points and foreshortening factor

I'm working on creating a homography 3x3 matrix to do a perspective correction of a photograph 2D piece of paper. The paper contains 3 markers (like the 3 corner markers of a QR code) in its corners, ...
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### Upper bound on Frobenius norm of inverse of positive definite, symmetric matrix

Let $\Sigma$ be a symmetric, positive definite $n \times n$ matrix. I want an upper bound on the Frobenius norm of $\Sigma^{-1}$ that does not involve calculating the determinant of $\Sigma$. The ...
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### Determine and classify all equilibrium points of this non-linear DE

Consider the DE $\begin{cases} \dot{x}=-2x(x-1)(2x-1)\\ \dot{y}=-2y \end{cases}$. Determine all equilibrium points and classify these. Choose between a saddle point, (in)stable nod, center or a (in)...
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### Books with similar coverage to Linear Algebra Done Wrong

Axler's book is great, but for my immediate purposes, it isn't suitable. I've been looking at the Table of Contents of Linear Algebra Done Wrong by Treil starting at p. 5 of this document but there's ...
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### If $0 \in W(A)\mathop \Rightarrow \limits^? W(A) = \left\{ {{x^*}Ax:x \in {C^n},{x^*}x \le 1} \right\}$

Let $A\in M_n$ and $W(A)$ be numerical range of $A$. Suppose $0\in W(A)$. Why does $W(A) = \left\{ {{x^*}Ax:x \in {C^n},{x^*}x \le 1} \right\}$?
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### How to do a Hermitian matrix decomposition?

I want to recover the matrix $A$ out of the Hermitian matrix $H$ such that: $$H = A\cdot A'$$ where : $H$ is a hermitian matrix. $A$ is a non-square matrix. $A'$ is the conjugate transpose of the ...
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### Linear programming of integers

Suppose that we have a linear programming problems involving two integer variables. Many textbooks state that the optimal solution will occur at the corner point. However, what if the corner point ...
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### Subalgebras of matrices property

Let $g$ be a Lie subalgebra of $gl_n(\mathbb{C})$ which has the propety that if $a\in g$ then also $a^\dagger\in g$ (where $a^\dagger$ is conjugate transpose). I want to show that if $a$ is an ideal ...
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### The variance of a sum of random vectors

There are $n$ vectors each containing exactly $q$ random variables as elements. Each vector is denoted I$_k$. Each variable within the vector has its own (normal) probability distribution, and the ...
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### Reference for the “geometry” or “arrangements” of subspaces of a vector space?

Inspired by Section $5$ of Chapter $1$ in Kostrikin & Manin's famous "Linear Algebra and Geometry", I am searching for a book or paper on the geometry or arrangement of subspaces in a finite-...
Let $\mathbf{v}$ be an $N$-dimensional binary vector. The first $m$ coordinates of $\mathbf{v}$ belong to a category, termed as "category a", and the last $n$ ($=N-m$) coordinates belong to another ...