矩阵转换表示(翻译).docx

This article copy form MSDN 2001. mk:@MSITStore:C:\Program%20Files\Microsoft%20Visual%20Studio\MSDN\2001OCT\1033\gdicpp.chm::/hh/gdicpp/cpp_aboutgdip05_00c4.htmPlatform?SDK:?GDI+ Translate By guozhengkun转换矩阵表示一个m×nmatrix is a set of numbers arranged in m rows and n columns. The following illustration shows several matrices.一个m×n矩阵是m行n列的一组数字集合。下图列出了几种矩阵。You can add two matrices of the same size by adding individual elements. The following illustration shows two examples of matrix addition.你可以通过矩阵每个元素相加实现两个大小相同的矩阵的加法运算An m×n matrix can be multiplied by an n×p matrix, and the result is an m×p matrix. The number of columns in the first matrix must be the same as the number of rows in the second matrix. For example, a 4×2 matrix can be multiplied by a 2×3 matrix to produce a 4×3 matrix.一个m×n矩阵乘以n×p矩阵, 结果是m×p矩阵. 第一个矩阵的列数必须和第二个矩阵的行数相同才能相乘。举例，一个 4×2 矩阵可以通过一个 4×3 矩阵乘以 2×3 矩阵得到。Points in the plane and rows and columns of a matrix can be thought of as vectors. For example, (2, 5) is a vector with two components, and (3, 7, 1) is a vector with three components. The dot product of two vectors is defined as follows:平面上的点集和矩阵的行列可以看作向量的集合。例如，(2, 5)是一个包含两个分量的向量，and (3, 7, 1) 是一个包含三个分量的向量。两个向量的点积定义如下：(a, b) ? (c, d) = ac + bd(a, b, c) ? (d, e, f) = ad + be + cfFor example, the dot product of (2, 3) and (5, 4) is (2)(5) + (3)(4) = 22. The dot product of (2, 5, 1) and (4, 3, 1) is (2)(4) + (5)(3) + (1)(1) = 24. Note that the dot product of two vectors is a number, not another vector. Also note that you can calculate the dot product only if the two vectors have the same number of components.例如， (2, 3) 和 (5, 4) 的点积等于 (2)*(5) + (3)*(4) = 22。 (2, 5, 1) 和 (4, 3, 1) 等于 (2)(4) + (5)(3) + (1)(1) = 24。注意两个向量的点积是一个数值，不是另一个向量。另外，注意只有分量个数相同的向量才能计算点积。Let A(i, j) be the entry in matrix A in the ith row and the jth column. For example A(3, 2) is the entry in matrix A in the 3rd row and the 2nd column. Suppose A, B, and C are matrices, and AB = C. The entries of C are calculated as follows:假定A(i, j)是矩