# Matrix Algebra (Econometric Exercises) ## 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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