Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

Matrix Algebra - Fundamentals

The following are a few basic definitions concerning matrices.

Definition. A matrix is a rectangularly shaped array with m rows and n columns of mn mathematical objects of a given basic set.

The order of a matrix is mn ("m by n"). Each column and each row of a matrix defines a vector. A column vector is nothing other than an m1 matrix, and a row vector is a 1n matrix.

Matrices are denoted by bold uppercase letters, e.g.  A. Matrix elements are denoted by lowercase letters subscripted by two indices, i.e. am,n. Sometimes the comma between the indices is omitted. The sequence of the indices is not arbitrary; the first index always denotes the row, the second index the column. If m=n, the matrix is called a square matrix of order n. If a matrix is square, the diagonal containing elements of equal indices (a11, a22, ..., ann) is called the principal diagonal of this matrix. The trace of a matrix is the sum of all elements of the principal diagonal.