Linear Algebra

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Linear algebra is study of linear systems of equations and their transformation properties.

Linear algebra is a college-level concept and course.


Lie Group: A Lie group is a differentiable manifold that has the structure of a group and that satisfies the additional condition that the group operations of multiplication and inversion are continuous.
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.
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
  • Matrix Inverse
  • Eigenvector
  • Matrix Multiplication
  • Euclidean Space
  • Norm
  • Inner Product