Explore Norm on MathWorld

A norm is a quantity that describes the length, size, or extent of a mathematical object.

Norm is a college-level concept that would be first encountered in a linear algebra course.


Absolute Value: The absolute value of a number is the distance of the number from the origin.


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.
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.
Vector: (1) In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. (2) In topology, a vector is an element of a vector space.
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.

Classroom Articles on Linear Algebra (Up to College Level)

  • Eigenvalue
  • Linear Transformation
  • Eigenvector
  • Matrix Inverse
  • Euclidean Space
  • Matrix Multiplication
  • Linear Algebra