蚌埠医学院：《多元统计分析》（双语版） 第二讲 多元统计分析理论基础

Data Matrices and Manipulation

zf Data Matrices and Manipulation

Presentation outline ☆1、 Matrices and vectors ☆2、 Random vector 今3、 Multivariate data matriⅸx 4, Population mean vector, covariance and correlation matrices %5. Sample mean vector, covariance and correlation matrices &6, Euclidean, statistical and mahalanobis distances 2021/2/22 2

2021/2/22 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

I Matrices and vectors B A matrix of size n xp is a rectangular array of numbers with n rows and p columns of the form(n行p列矩阵) 11212 2021/2/22

2021/2/22 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 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 2021/2/22 4

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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= A b= B 25 3×2 2021/2/22 5 cxt

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令Ifn=p, then this is a square matrix(方阵) A 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 r.(行向量) R=[2 2021/2/22 6 cxt

2021/2/22 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）

令 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 C-Is,c.c R 4-4- 2021/2/22 cxt

2021/2/22 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:

◆例:给定一个矩阵A, a b c d 矩阵A的转置矩阵是?? a c A 2021/2/22 8

2021/2/22 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) 100 020 005 2021/2/22 cxt

2021/2/22 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          

o 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) 23 23 2021/2/22 10 cxt

2021/2/22 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）