# Questions tagged [linear-algebra]

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 concerning matrices, use the (matrices) tag. For questions specifically concerning matrix equations, use the (matrix-equations) tag.

82,524 questions
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### Set of real valued functions defined and continuous on closed interval $[0,1]$ [on hold]

Prove that $C[0,1]$ such that $f(3/4)=0$ is not a vector space?
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### Find the eigenvalues of a polynomial transformation

Say $$F_2[X]:=\{p(x)=ax^2+bx+c:a,b,c \in F\}$$ And the linear operator T:$F_2[X] \to F_2[X]$ defined as: $$T(ax^2+bx+c)=(2a+6b+5c)-(8a+b)x+(c-2a)x^2$$ How can I find the eigenvalues and ...
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### Geometric proof for Composition bound property of operator norms?

This is just a curiosity. For linear transformations $A$ and $B$, $||AB|| \le ||A|| \cdot ||B||$ where$||\cdot||$ denotes the operator norm (Of course provided $AB$ exists.) This fact has a proof, but ...
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### Reformulating a high-rank linear system into a block-matrix equation

I have on my hands a linear system of equations of the following form $$\sum_{j=1}^K\sum_{q=1}^N A_{ijpq} x_{jq} = b_{ip} \quad(i=1\dots K,p=1\dots N)$$ in which the $x_{jq}$ are unknown and the ...
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### Burning a rope to count time

A rope burns irregularly in 16 minutes and costs 32 rupees, while a second rope burns also irregularly in 7 minutes and costs 14 rupees. Both can be lit only at one end and can be turned off and lit ...
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### Proving infeasibility using Duality

suppose we have the linear program min{$c^Tx: Ax \leq 0, x \leq 0$} and its corresponding dual max{$0^Tx: A^Ty \geq 0, y \leq 0$}. How can we show that the Dual is infeasible? I started by ...