Explore Determinant on MathWorld

The determinant of a square matrix is a scalar (commonly computed using so-called expansion by minors) which is nonzero if and only if the matrix has an inverse.

Determinant is a high school-level concept that would be first encountered in a pre-calculus course. It is listed in the California State Standards for Linear Algebra.


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 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 Pre-Calculus (Up to High School Level)

  • Asymptote
  • Logarithm
  • Complex Conjugate
  • Natural Logarithm
  • Complex Number
  • Normal Vector
  • Complex Plane
  • Parabola
  • Conic Section
  • Parametric Equations
  • Cross Product
  • Plane
  • Curve
  • Plane Curve
  • Domain
  • Polar Coordinates
  • Dot Product
  • Range
  • e
  • Rational Function
  • Ellipse
  • Reflection
  • Exponential Function
  • Rotation
  • Function
  • Rotation Matrix
  • Hyperbola
  • Scalar
  • i
  • Spherical Coordinates
  • Imaginary Number
  • Tangent Line
  • Inverse Function
  • Translation
  • Locus
  • Vector