《多元统计分析》多元统计分析理论基础，矩阵和多元正态分布2

Data Matrices and Manipulation

zf Data Matrices and Manipulation

Presentation outline ◆1、 Matrices and vectors 令2、 Random vector 3 Multivariate data matrix 4, Population mean vector, covariance and correlation matrices %s 5, Sample mean vector, covariance and correlation matrices 6. Euclidean statistical and mahalanobis distances 2021/1/21

2021/1/21 2 cxt 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

1、 Matrices and vectors %o a matrix of size n xp is a rectangular array of numbers with n rows and p columns of the fom(n行p列矩阵) 息 4=a1a2…马 息 2021/1/21 xt

2021/1/21 3 cxt 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） 

表一 表二 语文数学 语文数学 85 80 88 83 甲乙丙 90 82 甲乙丙 92 85 75 63 76 66 2021/1/21

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这两个长方形数表都叫做矩阵,并简记为 8580 8883 A=9082,B=9285 7563 7666 矩阵A和B都具有3行2列,故称为3×2矩阵 记为 A=A32,B=B32 2021/1/21 cXt

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☆Ifn=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) o If there is only one row, then this is called a row vector.(行向量) R=[ I 2021/1/21

2021/1/21 6 cxt ❖ 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）

冷 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 andr above are t4ma…anC=e1"c]R≈/ F 2021/1/21 cXt

2021/1/21 7 cxt ❖ 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:

令例:给定一个矩阵A, a b A c d 矩阵A的转置矩阵是?? a c b d 2021/1/21

2021/1/21 8 cxt ❖ 例：给定一个矩阵A， 矩阵A的转置矩阵是？？

其他特殊矩阵形式和定义: 令 a zero matrix has all elements equal to zero.(零 矩阵) (000 000 000 .o a diagonal matrix is a square matrix that has elements of zero, except down the main diagonal (对角矩阵) 00 020 005 2021/1/21 cXt

2021/1/21 9 cxt 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） 000 000 000           1 0 0 0 2 0 0 0 5          

A symmetric matrix is a square matrix that is unchanged when it is transposed I. e.A'=A.(对称矩 阵一矩阵的转置和它本身相等) 12)(12 23)(23 2021/1/21 10 cXt

2021/1/21 10 cxt ❖ A symmetric matrix is a square matrix that is unchanged when it is transposed I.e. A’=A.（对称矩 阵—矩阵的转置和它本身相等）