# 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.

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### Integer matrices with integer inverses

If all entries of an invertible matrix $A$ are rational, then all the entries of $A^{-1}$ are also rational. Now suppose that all entries of an invertible matrix $A$ are integers. Then it's not ...
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### Applying a linear transformation to time sequences to separate interfering oscillations

This is an applied problem, which arises from the problem of reorienting of a sensor axes according to particle displacement directions: Consider a sensor which is located inside the solid substance. ...
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### A solution for equation with N unknowns with specific constraints?

I am working with granular materials (seeds). I am looking for a way to correctly scale the amount of different particles in one batch using weight only. I have worked with the problem a bit and ...
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### How many presentable boolean functions with n attributes are linear separable?

The aim is to find a formula for the question. For n=2 i get (2^(2^n)=16 possible functions. This is the solution for a boolean function with 2 attributes: ...
$U$ and $W$ are two subspaces of vector space $V$. If $U \oplus W = V$, then $\forall v \in V$, there exist two unique vectors $u \in U$ and $w \in W$ such that $v = u + w$. Is the reverse true? ...