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The publication in English of Gantmacher's book ‘The Theory of Matrices’ is of particular interest in that it reveals to us the standard attained by a Russian textbook in that particular field. If this book is typical of the standard of other Russian mathematical works, the translation of many more of them would be something to be warmly welcomed. The translator, Professor K. A. Hirsch, is himself an outstanding authority on matrix theory, and the fact that he has undertaken the translation is in itself a compliment to the original book. It takes only a little reading to reveal that the translation has been performed with felicity and that the style is all that can be desired.

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