Mr. Integral
Math notes/Linear Algebra/Vectors, Matrices and Systems

Matrix Products, Inverses and LU — Cheat sheet

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Core rule

(AB)x=A(Bx)(AB)\mathbf x=A(B\mathbf x). Solve LUx=bLU\mathbf x=\mathbf b by forward then backward substitution; with swaps use PA=LUPA=LU.

Watch for

Multiplication is generally not commutative. Not every square matrix has an inverse.