Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different manner than the usual textbook. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text.

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Let X₀ be a square matrix (complex or otherwise) and u₀ a (normalized) eigenvector associated with an eigenvalue λ^o of X₀, so that the triple (X₀, u₀, λ₀) satisfies the equations Xu = λu, . We investigate the conditions under which unique differentiable functions λ(X) and u(X) exist in a neighborhood of X₀ satisfying λ(X₀) = λ_O, u(X₀) = u₀, X_u = λu, and . We obtain the first and second derivatives of λ(X) and the first derivative of u(X). Two alternative expressions for the first derivative of λ(X) are also presented.

This article tests whether points in tennis are independent and identically distributed (iid). We model the probability of winning a point on service and show that points are neither independent no...