The study of vector spaces, matrix operations, and linear transformations between them.
core objects:: vectors, matrices, tensors
eigenvalues and eigenvectors reveal invariant directions under transformation
determinant measures volume scaling; rank measures dimensional span
The spectral theorem decomposes symmetric matrices into orthogonal eigenbases
Foundation of machine learning, quantum mechanics, signal processing, and optimization
singular value decomposition generalizes eigendecomposition to rectangular matrices
inner product defines angles and distances, enabling geometry in arbitrary dimensions
Related:: calculus, statistics, fourier transform, differential equations, category theory