1. Rectangular arrays -- Equality of matrices -- Addition and subtraction of matrices -- Multiplication by a scalar -- Vectors -- Vector representation of a system of linear equations -- Inner products -- Matrix-vector multiplication -- Matrix multiplication -- Examples of the use of matrix multiplication -- The identity matrix -- 2. Elementary operations and the inverse of a matrix -- Elementary operations -- Echelon matrices -- The inverse of a square matrix -- A procedure to calculate the inverse of a matrix if it exists -- Application of the inverse of a matrix to the solution of a system of equations -- Application in regression analysis -- Application in input-output analysis -- 3. More about simultaneous linear equations -- Linear dependence among a set of vectors -- The rank of a matrix -- Examples -- Simultaneous linear equations -- The full-rank case -- The less than full-rank case and the generalized inverse -- Homogeneous equations -- 4. Eigenvalues and eigenvectors -- Determinants -- Eigenvalues and eigenvectors -- Principal components -- Symmetric matrices
Summary
Defines basic terms and elementary matrices manipulation, introduces the concept of linear dependence, and explains eigenvalues and eigenvectors with illustrated examples
Analysis
Algebra Matrices
Notes
(Sage university papers. Quantitative applications in the social sciences ; no. 07-038)