A vector is a quantity characterised by both a magnitude and a direction, in contrast to a scalar, which is described by magnitude alone.

A matrix is a rectangular array of real numbers arranged in rows and columns. A matrix with m rows and n columns is said to have dimensions m \times n, and is called an m \times n matrix.

To every square matrix of order n one can associate a real number called the determinant of the matrix, denoted det ( A ) or | A |.

The rank of a matrix A, denoted r ( A ) or rank ( A ), is the maximum number of linearly independent rows (or equivalently, columns) of A.

In linear algebra, a linear combination is the fundamental operation that relates vectors to one another within a given collection.

A linear transformation, represented by a square matrix A, acts on vectors by moving them in space. It can stretch, compress, rotate, or reflect them, and in general the image of a vector points in a...

A square matrix is said to be diagonalizable when it is possible to find a basis of the underlying vector space consisting entirely of eigenvectors of that matrix.