Matrix

A Matrix is a Data Structure ...

• AKA: Number Matrix, Matrix (Mathematics).
• Context:
  • It can be a Vector of (equal sized) Numeric Vectors.
  • It can be:
    • an Identity Matrix.
    • a Square Matrix.
  • It can be an input to:
    • Matrix Multiplication
    • Matrix Factorization
  • It can have an Eigenvalue.
• See: Array Data Structure, Eigenvector, Linear Algebra.

References

2009

• (Wikipedia, 2009) http://en.wikipedia.org/wiki/Matrix_(mathematics)
  • In mathematics, a matrix (plural matrices) is a rectangular array of numbers, as shown at the right. In addition to a number of elementary, entry-wise operations such as matrix addition a key notion is matrix multiplication. The latter operation connects matrices to linear transformations, i.e. higher-dimensional analogs of linear functions, i.e., functions of the form f(x) = c · x, where c is a constant. This map corresponds to a matrix with one row and column, with entry c. In general matrices are used to keep track of the coefficients of linear equations and to record other data that depend on multiple parameters. This concept was also one of the historical roots of matrices.
  • In the particular case of square matrices, matrices with equal number of columns and rows, more refined data are attached to matrices, notably the determinant, inverse matrices, which both govern solution properties of the system of linear equation belonging to the matrix, and eigenvalues and eigenvectors.
  • Matrices are described by the field of matrix theory. The close relationship of matrices with linear transformations makes the former a key notion of linear algebra. Other types of entries, such as elements in more general mathematical fields or even rings are also used. Matrices consisting of only one column or row are called vectors, while higher-dimensional, e.g. three-dimensional, arrays of numbers are called tensors.