mathematics//linear algebra

Linear algebra describes linear combinations, vector spaces and the transformations that preserve those combinations. A matrix represents a transformation in chosen coordinates; multiplying it by a vector computes the transformed coordinates. Changing the basis changes the representation without necessarily changing the underlying operation.

Linear algebra describes linear combinations, vector spaces and the transformations that preserve those combinations. A matrix represents a transformation in chosen coordinates; multiplying it by a vector computes the transformed coordinates. Changing the basis changes the representation without necessarily changing the underlying operation.

This makes matrices useful for coupled system models, where many scalar relationships can be collected into one equation. Eigenvalues describe special directions of a transformation, while linearization explains how a nonlinear model can yield a local linear approximation.