Linear Algebra in Physics: Matrices, Vectors, and States

Linear algebra studies vectors and matrices, the math tools that handle many quantities at once.
In physics, vectors represent forces, velocities, and fields that have both size and direction.
Matrices rotate, stretch, or transform vectors, just like forces reshape motion.
Quantum mechanics uses vectors (state vectors) to describe particles’ possible states.
Matrices called operators act on these states to predict measurable outcomes.
Eigenvalues and eigenvectors reveal stable states of systems, from atoms to oscillators.
Relativity relies on tensors—generalized matrices—to describe spacetime geometry.
Computer simulations in physics use linear algebra to handle millions of variables efficiently.
Symmetry groups in particle physics are expressed through matrix algebra.
At its core, linear algebra organizes the universe’s rules into elegant mathematical structures.