**Colloquium Publications**

Volume: 17;
1934;
205 pp;
Softcover

MSC: Primary 15;

Print ISBN: 978-0-8218-4610-0

Product Code: COLL/17

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

**Electronic ISBN: 978-0-8218-3204-2
Product Code: COLL/17.E**

List Price: $50.00

AMS Member Price: $40.00

MAA Member Price: $45.00

# Lectures on Matrices

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*J. H. M. Wedderburn*

It is the organization and presentation of the material, however, which make the peculiar appeal of the book. This is no mere compendium of results—the subject has been completely reworked and the proofs recast with the skill and elegance which come only from years of devotion.

—Bulletin of the American Mathematical Society

The very clear and simple presentation gives the reader easy access to the more difficult parts of the theory.

—Jahrbuch über die Fortschritte der
Mathematik

In 1937, the theory of matrices was seventy-five years
old. However, many results had only recently evolved from special
cases to true general theorems. With the publication of his Colloquium
Lectures, Wedderburn provided one of the first great syntheses of the
subject. Much of the material in the early chapters is now familiar
from textbooks on linear algebra. Wedderburn discusses topics such as
vectors, bases, adjoints, eigenvalues and the characteristic
polynomials, up to and including the properties of Hermitian and
orthogonal matrices. Later chapters bring in special results on
commuting families of matrices, functions of matrices—including
elements of the differential and integral calculus sometimes known as
matrix analysis, and transformations of bilinear forms. The final
chapter treats associative algebras, culminating with the well-known
Wedderburn–Artin theorem that simple algebras are necessarily
isomorphic to matrix algebras.

Wedderburn ends with an appendix of historical notes on the
development of the theory of matrices, and a bibliography that
emphasizes the history of the subject.

#### Readership

Graduate students and research mathematicians interested in matrices.

#### Table of Contents

# Table of Contents

## Lectures on Matrices

- Cover Cover11
- Title page i2
- Preface iii4
- Contents v6
- Corrigenda ix10
- Chapter I. Matrices and vectors 112
- Chapter II. Algebraic operations with matrices. The characteristic equation 2031
- Chapter III. Invariant factors and elementary divisors 3344
- Chapter IV. Vector polynomials. Singular matric polynomials 4758
- Chapter V. Compound matrices 6374
- Chapter VI. Symmetric, skew, and hermitian matrices 8899
- Chapter VII. Commutative matrices 102113
- Chapter VIII. Functions of matrices 115126
- Chapter IX. The automorphic transformation of a bilinear form 140151
- Chapter X. Linear associative algebras 147158
- Appendix I. Notes 169180
- Appendix II. Bibliography 172183
- Index to bibliography 194205
- Index 197208
- Back Cover Back Cover1217