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Matrix Algebra from a Statistician's Perspective
Preface.
- Matrices.
- Submatrices and partitioned matricies.
- Linear dependence and independence.
- Linear spaces: row and column spaces.
- Trace of a (square) matrix.
- Geometrical considerations.
- Linear systems: consistency and compatability.
- Inverse matrices.
- Generalized inverses.
- Indepotent matrices.
- Linear systems: solutions.
- Projections and projection matrices.
- Determinants.
- Linear, bilinear, and quadratic forms.
- Matrix differentiation.
- Kronecker products and the vec and vech operators.
- Intersections and sums of subspaces.
- Sums (and differences) of matrices.
- Minimzation of a second-degree polynomial (in n variables) subject to linear constraints.
- The Moore-Penrose inverse.
- Eigenvalues and Eigenvectors.
- Linear transformations.
- References.
- Index.
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