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# linear\_algebra

## Basic idea

Study of vector spaces and linear maps between them. Matrices give a concrete representation of linear maps in a chosen basis.

## Key formulas

* Matrix-vector product: $(Ax)*i=\sum\_j A*{ij}x\_j$
* Linear system: $Ax=b$
* Eigenvalue equation: $Av=\lambda v$
* Determinant nonzero $\iff$ matrix invertible