This document discusses linear transformations and matrices. It introduces how linear transformations on physical quantities are usually described by matrices, where a column vector u representing a physical quantity is transformed into another column vector Au by a transformation matrix A. As an example, it discusses orthogonal transformations, where the transformation matrix A is orthogonal. It proves that for an orthogonal transformation, the inner product of two vectors remains invariant. It also discusses properties of other types of matrices like Hermitian, skew-Hermitian and unitary matrices.