Matrix Algebra: Exercises and Solutions (Paperback, Softcover Repri)

1 Matrices.- 2 Submatrices and Partitioned Matrices.- 3 Linear Dependence and Independence.- 4 Linear Spaces: Rowand Column Spaces.- 5 Trace of a (Square) Matrix.- 6 Geometrical Considerations.- 7 Linear Systems : Consistency and Compatibility.- 8 Inverse Matrices.- 9 Generalized Inverses.- 10 Idempotent Matrices.- 11 Linear Systems: Solutions.- 12 Projections and Projection Matrices.- 13 Determinants.- 14 Linear, Bilinear, and Quadratic Forms.- 15 Matrix Differentiation.- 16 Kronecker Products and the Vec and Vech Operators.- 17 Intersections and Sums of Subspaces.- 18 Sums (and Differences) of Matrices.- 19 Minimization of a Second-Degree Polynomial (in n Variables) Subject to Linear Constraints.- 20 The Moore-Penrose Inverse.- 21 Eigenvalues and Eigenvectors.- 22 Linear Transformations.- References.