enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Matrix (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Matrix_(mathematics)

    Others, such as matrix addition, scalar multiplication, matrix multiplication, and row operations involve operations on matrix entries and therefore require that matrix entries are numbers or belong to a field or a ring. [8] In this section, it is supposed that matrix entries belong to a fixed ring, which is typically a field of numbers.

  3. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    If the scalars have the commutative property, then all four matrices are equal. More generally, all four are equal if c belongs to the center of a ring containing the entries of the matrices, because in this case, cX = Xc for all matrices X. These properties result from the bilinearity of the product of scalars:

  4. List of named matrices - Wikipedia

    en.wikipedia.org/wiki/List_of_named_matrices

    A number of matrix-related notions is about properties of products or inverses of the given matrix. The matrix product of a m-by-n matrix A and a n-by-k matrix B is the m-by-k matrix C given by (), = =,,. [2] This matrix product is denoted AB.

  5. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    A basic 3D rotation (also called elemental rotation) is a rotation about one of the axes of a coordinate system. The following three basic rotation matrices rotate vectors by an angle θ about the x-, y-, or z-axis, in three dimensions, using the right-hand rule—which codifies their alternating signs.

  6. Transformation matrix - Wikipedia

    en.wikipedia.org/wiki/Transformation_matrix

    In other words, the matrix of the combined transformation A followed by B is simply the product of the individual matrices. When A is an invertible matrix there is a matrix A −1 that represents a transformation that "undoes" A since its composition with A is the identity matrix. In some practical applications, inversion can be computed using ...

  7. General linear group - Wikipedia

    en.wikipedia.org/wiki/General_linear_group

    In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication.This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with the identity matrix as the identity element of the group.

  8. Determinant - Wikipedia

    en.wikipedia.org/wiki/Determinant

    For matrices over non-commutative rings, multilinearity and alternating properties are incompatible for n ≥ 2, [48] so there is no good definition of the determinant in this setting. For square matrices with entries in a non-commutative ring, there are various difficulties in defining determinants analogously to that for commutative rings.

  9. Idempotent matrix - Wikipedia

    en.wikipedia.org/wiki/Idempotent_matrix

    Toggle Properties subsection. 3.1 Singularity and regularity. 3.2 Eigenvalues. ... In linear algebra, an idempotent matrix is a matrix which, when multiplied by ...