Linear algebra

Linear algebra is the math of vectors (lists of numbers, like a point or a direction) and matrices (grids of numbers that transform vectors). The most useful way to think of a matrix is as an action: it rotates, stretches, squashes or flips space, and multiplying matrices chains those actions together. Eigenvectors are the special directions a matrix only stretches without turning, and they reveal its essential behavior. Decompositions like SVD break any matrix into simple rotate-stretch-rotate steps, which powers compression and recommendations. Linear algebra underlies graphics, robotics, statistics and machine learning, where nearly every computation is matrix multiplication at scale.