topics: |  math | linear-algebra

This book entered my consciousness when I encountered it at the Half-Price Books store at College Station around 1993. It cost me all of 50 c, and I looked upon it as a sort of dead background read. Across continents, it languished on the shelf.

Much later, when I took it up one day, it was intriguing to discover that in 1959, the terms "eigenvalue" / "eigenvector" had not yet been standardized; the translator calls them proper numbers and proper vectors of a matrix.

Even later, I realized that this text had become a classic. It is listed as the first text referred to by Golub and van Loan as "Classic" texts in linear algebra.

Several decades after the book had been hiding in my shelves, I realized that Vera Nikolaevna Faddeeva (1906-1983) was an woman, one of the early pioneering women mathematicians.

from the Translator's Note:
	I have replaced many of the Russian references with more accessible
	ones, and re-computed all of the principal tables, which I hope will
	thus be [more] reliable.  p.vi

Contents

   Preface
   Translator's note
1. Basic material from linear algebra 			  1
2. Systems of linear equations 				 63
3. The proper numbers and proper vectors of a matrix 	147
   Bibliography

Danilevsky's method for eigen-computation:
	http://web.ist.utl.pt/~ist11038/compute/com/,eigen/FaddeevaDanil.pdf

bio

		http://www-history.mcs.st-and.ac.uk/Biographies/Faddeeva.html



Vera Nikolaevna was born in Tambov, a town about 470 km south east of
Moscow.  In 1930, she married the mathematician Dmitrii Konstantinovich
Faddeev [Faddeeva is her married name).

The years during which Vera Nikolaevna was an undergraduate at Leningrad
State University were ones of great difficulty for the academics at the
university. During this period independent thinkers were persecuted and N M
Gyunter, at that time President of the Leningrad Mathematical Society and a
man with a reputation for courage and independent thought, was in great
danger. In fact the Leningrad Mathematical Society was disbanded in 1930
following a proposal by the vice-president Vladimir Ivanovich Smirnov, in a
successful attempt to save Gyunter's life and the lives of other
mathematicians.

Background to the book

Reviewing Faddeeva's classic 1950 book Computational methods of linear
algebra, G E Forsythe writes:-

	This is a textbook on numerical methods for solving finite systems of
	linear equations, inverting matrices, and calculating the eigenvalues
	of finite matrices, all with desk calculators. Although the book is
	far from exhaustive, the mathematical elegance, the breadth of
	material, and the number of error-free numerical examples make this
	by far the finest book to appear in the field.

The first chapter of this book was translated into English for the National
Bureau of Standards in the United States in 1952 and, in 1959, an English
translation of the whole book was published. [12]:-

	The first chapter of this book forms a clear and well-written
	introduction to the elementary parts of linear algebra. The second
	chapter deals with numerical methods for the solution of systems of
	linear equations and the inversion of matrices, and the third with
	methods for computing characteristic roots and vectors of a
	matrix. Most of the important material in these domains is to be
	found here, and many numerical examples which illustrate the
	algorithms and point out their merits and deficiencies are given. The
	discussion is directed principally to the hand computer, and machine
	computation in the modern sense is hardly present, but the book must
	be regarded as a valuable guide for the worker in the general area of
	linear computation.

Olga Taussky-Todd, after giving a similar guide to the contents, writes that
the book will serve [13]:-

	... a very useful purpose for researchers, as well as for teachers
	and students of numerical analysis, because of the clear presentation
	of the basic facts.
Alston Householder [1] writes:-

	Each edition was, at the time of its appearance, by far the most
	complete and up-to-date treatment of the subject in print.

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