Linear Algebra
The mathematical discipline studying vector spaces, linear transformations, matrices, and systems of linear equations.
Governing formula
A x = b, v · w = ∑ v_i w_i
SI unit
Vector Spaces & Matrices
In depth
Linear algebra provides the core framework for multi-dimensional physics modeling. Quantum state vectors reside in Hilbert space, coordinate rotations use orthogonal matrices, and coupled systems solve linear equations.
Examples in the real world
Solving coupled harmonic oscillator systems and diagonalizing Hamiltonian matrices in quantum chemistry.