# 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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### Positive values of Quadratic Form with nonnegative vectors

I hope somebody can give me a hint on the following problem: Consider a real valued $n \times n$ matrix $A$. Let $x$ be a real-valued "non-negative" vector, i.e. a vector with nonnegative components,...
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### matrix multiplied by rotation matrix on right side and transpose(rotation) on left side

Would a matrix remain un-rotated if it is multiplied by an orthonormal rotation matrix on right side and transpose of same rotation matrix on the left side?
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### Linear Algebra Eigenvalues and Eigenvectors [closed]

So I have a 2x2 matrix where equation 1(EQN1) is 1 and 2; equation2(EQN2) 2: 4 and 3 The determinant is det(A-λI)=0 When I first solve the eigenvalues I get λ=5, λ=-1 Now this is where I am lost,...
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### Solve for $x,y,z$ from the linear equations.

The main question is : \begin{align} (b+c)(y+z)-ax &= b-c \tag{1} \\ (c+a)(z+x)-by &= c-a \tag{2} \\ (a+b)(x+y)-cz &= a-b \tag{3}\\ \end{align} Solve for $x,y,z$ if $a+b+c\ne0$ ...
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### About the distributive property of matrices

So We all know that matrix operations are distributive, so here is my question.$A^2+AB\\$ and $BA+B^2$ is two matrix operations I have, I know we can do $A(A+B)$ in the first operation but I'm not ...
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### Matrix decomposition into square positive integer matrices

This is an attempt at an analogy with prime numbers. Let's consider only square matrices with positive integer entries. Which of them are 'prime' and how to decompose such a matrix in general? To ...
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### May I Know a Algorithm to compute generator polynomial coefficients for RS codes (255,245,t=5) in GF(256)

May I Know a Algorithm to compute generator polynomial coefficients for RS codes (255,245,t=5) in GF(256) ? I want to write a program to compute generator polynomial coefficients for RS codes (255,...
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### Basis of tensor product of subspaces

Consider two vector spaces $S$ and $S\otimes S$, both of which are subspaces of $H\otimes H$, where $H$ is of $d$ dimension and so $H\otimes H$ is of $d^2$ dimension. We assume that $S$ is of $n$-...
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### Identity relative to different orthonormal bases is unitary

Let $V$ be a finite-dimensional inner product space, and let $\beta,\beta'$ both be orthonormal bases for $V$. Is it the case that $[I]^{\beta'}_{\beta}$ is unitary? If so, how can we prove this? ...
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### Can a set of four vectors be a basis for P5?

From what I understand, you would need 3 vectors to form a basis of three dimensional space, but does this same restriction apply to a polynomial of let's say P5? In other words, if I'm given W={x^5, ...
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### confusion in a linear algebra theorem

Insights about $Tv_j=w_j$, the linear maps and basis of domain. I have a question about the theorem mentioned in the link above. I understand what the theorem is saying, but a little uncertain. it ...
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### Pseudo-inverse of matrix representation is matrix representation of pseudoinverse

Let $T: V \rightarrow W$ be a linear map on finite dimensional inner product spaces $V,W$. Let $\beta,\gamma$ be ordered (orthonormal?) bases for $V,W$ respectively. Is it necessarily the case that ...
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### Proving/verifying dimension and basis

I'm coming from a computer science background and am currently trying to formalize my linear algebra knowledge by going through Linear Algebra Done Right. I have an intuitive grasp on most of the ...
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### Derivation of gradient for non negative matrix factorization

I am looking at a paper for non-negative matrix factorization and can't seem to figure out the derivation for the gradient. The function is as follows: $f(W,H) = \frac{1}{2}||V-WH ||^2_F$ Where V ...
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### Which of the following are subspaces of $\mathbb{R}^3$?

I have two examples directly from my book: $$\{(x, y,z) : x + y + z = 1 \}$$ and $$\{(x, y, z) : x \leq y \leq z\}$$ The book once again isn't helping me understand the concept. What are the ...
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### I am confused by the statement “the null space of A is a nontrivial”

Correct me if I'm wrong but if a null space of a matrix A is nontrivial would it be correct to say that it is the opposite of the list of points in the Invertible Matrix Theorem? A is an invertible ...