Data Matrices and Manipulation zf Presentation Outline 1、Matrices and vectors 2、Random vector 3、Multivariate data matrix 4、Population mean vector, covariance and correlation matrices 5、Sample mean vector, covariance and correlation matrices 6、Euclidean, statistical and Mahalanobis distances zf 2 1、 Matrices and vectors A matrix of size n p is a rectangular array of numbers with n rows and p columns of the form( n 行 p列矩阵) zf 3 zf 4 zf 5 If n = p , then this is a square matrix(方阵). If a matrix has only one column, then this is called a column vector(列向量). If there is only one row, then this is called a row vector.(行向量) zf 6 Transpose of a Matrix(转置矩阵) denoted by a prime,is found by interchanging the rows and the columns.(将矩阵的行和列交换) The transpose of A, C and R above are: zf 7 例:给定一个矩阵A, 矩阵A的转置矩阵是?? zf 8 其他特殊矩阵形式和定义: A zero matrix has all elements equal to zero.(零矩阵)
A diagonal matrix is a square matrix that has elements of zero, except down the main diagonal.(对角矩阵) zf 9 A symmetric matrix is a square matrix that is unchanged when it is transposed . A’=A.(对称矩阵—矩阵的转置和它本身相等) zf 10
