Matrix Algebra - Karim M. Abadir, Jan R. Magnus - Google книги
Some results for triangular matrices; Schur's decomposition theorem and its consequences; Jordan's decomposition theorem; Positive Semi Definite and Idempotent Matrices: Positive semi definite matrices; Partitioning and positive semi definite matrices; Idempotent matrices; Part IX. Matrix Functions: Simple functions; Jordan representation; Matrix-polynomial representation; Part X.
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- Matrix Algebra (Econometric Exercises, Vol. 1)!
The Kronecker product; The vec-operator; The Moore-Penrose inverse; Linear vector and matrix equations; The generalized inverse; Part XI. Patterned Matrices, Commutation and Duplication Matrix: The commutation matrix; The symmetrizer matrix; The vec-operator and the duplication matrix; Linear structures; Part XII. Matrix Inequalities: Cauchy-Schwarz type inequalities; Positive semi definite matrix inequalities; Inequalities derived from the Schur complement; Matrix calculus: Basic properties of differentials; Scalar functions; Vector functions; Matrix functions; The inverse; Exponential and logarithm; The determinant; Jacobians; Sensitivity analysis in regression models; The Hessian matrix; Least squares and best linear unbiased estimation; Maximum likelihood estimation; Inequalities and equalities.
A stand-alone textbook in matrix algebra for econometricians and statisticians - advanced undergraduates, postgraduates and teachers. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text. The book should prove popular with students intent on teaching themselves and with instructors who wish to set challenging and educative exercises.
Books in the Econometric Exercises series
Recommended unequivocally to all parties. Besides basic topics, excellent treatment of matrix inequalities, vectorization, and matrix calculus. It belongs on every econometricians's bookshelf.
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Matrix Algebra (Econometric Exercises, Vol. 1)
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