This manual contains reference information about linear algebra and the properties of matrices. Theorems and matrix properties relating to eigenvalues and eigenvectors. Differentiating expressions involving matrices whose elements are functions of an independent variable. Statistical properties of vectors and matrices whose elements are random numbers. The geometric interpretation of a matrix property or theorem is generally described for 2 or 3 dimensions.
Theorems apply to real matrices or complex matrices of arbitrary shape unless explicitly stated.
Matrix dimensions are assumed to allow the sums and products in a theorem. All vectors are column vectors unless explicitly written as transposed. A matrix can be specified explicitly by listing its elements and using a semicolon to separate each row. Each row must have the same total number of columns and each matrix within a row must have the same number of rows. The matrix or vector 1 consists entirely of ones.