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. The matrix I denotes the square identity matrix with 1's down the main diagonal and 0's elsewhere. The matrix J denotes the square exchange matrix with 1's along the main anti-diagonal and 0's elsewhere.