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Constructive linear algebra

The value of such books as gentle introductions to the subject for the reader whose background is not a mathematical one is beyond doubt, but the mathematician can perhaps be forgiven for becoming a little impatient with them. I had hoped that I could describe Professor Vajda's book as offering a welcome counterbalance, and the contents list and a quick scan through the chapters did not diminish this hope: an opening chapter on convexity is succeeded by a treatment of the theory of linear inequalities, so paving the way for an account of linear programming and a little on quadratic programming; Chapter 4 explores optimality criteria in a more general context, and the final chapter is devoted to the study of duality. It was thus with a growing sense of disappointment that I found this hope to be unrealised as I read through the book. A little of the blame for this must be laid at the door of the printer: there are many errors and infelicities which reveal (not for the first time) this firm's inadequacies in mathematical typesetting; particularly tiresome errors have escaped correction on pp. 4,7,21,29 and 59. Professor Vajda's choice of notation sometimes fails to aid immediate comprehension: