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A transformation A ↦ P −1 AP is called a similarity transformation or conjugation of the matrix A. In the general linear group , similarity is therefore the same as conjugacy , and similar matrices are also called conjugate ; however, in a given subgroup H of the general linear group, the notion of conjugacy may be more restrictive than ...
The determinant of this matrix is −1, as the area of the green parallelogram at the right is 1, but the map reverses the orientation, since it turns the counterclockwise orientation of the vectors to a clockwise one. The determinant of a square matrix A (denoted det(A) or | A |) is a number encoding certain properties of the matrix.
[1] Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, [ 2 ] to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra , and as such has numerous applications in many areas of mathematics, as well as in ...
[1] Note that () has the same dimension as . A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question. A matrix polynomial identity is a matrix polynomial equation which holds for all matrices A in a specified matrix ring M n (R).
In linear algebra, an invertible matrix is a square matrix which has an inverse.In other words, if some other matrix is multiplied by the invertible matrix, the result can be multiplied by an inverse to undo the operation.
The Malaysian Matriculation Programme (Malay: Program Matrikulasi Malaysia) is a one-year pre-university preparatory programme [1] [failed verification] offered by the Ministry of Education, Malaysia.
In the first mechanism, Browner M.F. and colleagues [11] proposed the base-catalysis mechanism, carried out by the conserved glutamate residue and the Zn 2+ ion. In the second mechanism, the Matthews-mechanism, Kester and Matthews [ 12 ] suggested an interaction between a water molecule and the Zn 2+ ion during the acid-base catalysis .