By Paul E. Green (Auth.)
This booklet introduces matrix algebra to scholars in behavioral and administrative sciences. It in actual fact defines the relevance of the workouts to matters in the company neighborhood and the social and behavioral sciences. Readers will achieve a technical heritage for tackling applications-oriented multivariate texts
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Extra resources for Mathematical Tools for Applied Multivariate Analysis
Sample text
The transpose of a diagonal matrix is equal to the original matrix. 2. Sums and differences of diagonal matrices are also diagonal matrices. 3. Premultiplication of a matrix A by a diagonal matrix D results in a matrix in which each entry in a given row is the product of the original entry in A corresponding to that row and the diagonal element in the corresponding row of the diagonal matrix. To illustrate, D A DA 3 4 3 0 0 Il 2 0 2 0 2 1 0 0 l j L3 2 3 6 9 12 4 3 = 4 2 8 6 1 1 _3 2 1 1 4. Postmultiplication of a matrix A by a diagonal matrix D results in a matrix in which each entry in a given column is the product of the original entry in A corresponding to that column and the diagonal element in the corresponding column of the diagonal matrix.
5. The product of two symmetric matrices is not necessarily symmetric. Later chapters will discuss still other characteristics of symmetric matrices and the special role that they play in such topics as matrix eigenstructures and quadratic forms. 2 Diagonal, Scalar, Sign, and Identity Matrices A special case of a symmetric matrix is a diagonal matrix. A diagonal matrix is defined as a square matrix in which all off diagonal entries are zero. ) Entries on the main diagonal may or may not be zero.
Scalar multiplication is associative: *i(*2A) = (*i*2)A 5. Scalar multiplication is distributive: (ki + k2)A = kiA + k2A 6. There exists a null matrix (already defined) φ with the property that A+0= A 7. 4 and could be numerically illustrated in similar fashion. 4 Matrix Multiplication In discussing the multiplication of two (or more) matrices, conformability should first be pointed out. Similar to the previous discussion of matrix equality, addition, and subtraction, in which the matrices were assumed to be of common order before the relation or operation was meaningful, in multiplication the matrices must be con formable.