Matrix
Matrix | The MatrixThe two-dimensional table. The matrix are identified as NxM, where N is the number of rows in the table, M is the number of columns. In linear algebra is typically used in the square matrix (where the number of columns and rows is the same). In the 3D graph square matrices are used for the linear transformation vectors and points from one space to another.
The matrix can be multiply, invert (calculate the inverse matrix), as well as transposing - that is, to swap rows and columns (the line becomes the column and vice versa). A special kind of a square matrix - a single. In a single matrix of all elements, in addition to the main diagonal equal to zero, and the main diagonal (from the top left corner to the lower right) contains the units. A single matrix is equal to its inverse and ����������������� matrices. Multiplication of the matrix on hop count will result in exactly the same matrix.
Matrix multiplication is performed on the columns and rows for each element of the resulting matrix corresponding to this element of the string one scalar matrix is multiplied by the appropriate column on the other. The multiplication of matrices �������������� - that is, the matrices A and B work A * B does not necessarily equal to B * A.
You can also ����������� matrix and vector, if adhered to a certain conformity to their dimensions. There are two types of such multiplying - left and right. The left multiplies the NxM matrix to a vector-column in the dimension of M, and the result is a vector of dimension N. Right multiplies a vector-string dimension N of the matrix NxM, and the result is a vector of dimension of M. Vector-string is a vector of dimension n, recorded in a matrix of 1xN, vector-column is a vector of dimension M, recorded in the form of a matrix Mx1. In the rest of the multiplication rules are the same as for matrices is a string in the column. The right multiplication corresponds to the left with ����������������� matrix (and vice versa), and this property is often used in computer calculations for the various optimizations.
See also the Transformation, the Vector.