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Linear Transformation

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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.

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

Prerequisites

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 Algebra
  • Eigenvector
  • Matrix Inverse
  • Euclidean Space
  • Matrix Multiplication
  • Inner Product
  • Norm