Topics in a Linear Algebra Course

To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

Eigenvalue	An eigenvalue is one of a set of special scalars associated with a linear system of equations that describes that system's fundamental modes.
Eigenvector	An eigenvector is one of a special set of vectors associated with a linear system of equations.
Euclidean Space	Euclidean space of dimension n is the space of all n-tuples of real numbers which generalizes the two-dimensional plane and three-dimensional space.
Inner Product	(1) In a vector space, an inner product is a way to multiply vectors together, with the result being a scalar. (2) In vector algebra, the term inner product is used as a synonym for dot product.
Linear Algebra	Linear algebra is study of linear systems of equations and their transformation properties.
Linear Transformation	A function from one vector space to another. If bases are chosen for the vector spaces, a linear transformation can be given by a matrix.
Matrix	A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, for every linear transformation, there exists exactly one corresponding matrix, and every matrix corresponds to a unique linear transformation. The matrix is an extremely important concept in linear algebra.
Matrix Inverse	Given a matrix M, the inverse matrix is a new matrix M^-1 that when multiplied by M, gives the identity matrix.
Matrix Multiplication	Matrix multiplication is the process of multiplying two matrices (each of which represents a linear transformation), which forms a new matrix corresponding to the matrix representation of the two transformations' composition.
Norm	A norm is a quantity that describes the length, size, or extent of a mathematical object.
Vector Space	A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space.