Linear Algebra Gems: Assets for Undergraduate Mathematics, Vol. 59 Book

Foreword
Part 1- Partitioned Matrix Multiplication
Introduction; the Editors
Modern Views of Matrix Multiplication; the Editors
The Associativity of Matrix Multiplications; the Editors
Relationships Between AB and BA; the Editors
The Characteristic Polynomial of a Partitioned Matrix; D. Steven Mackey
The Cauchy-Binet Formula; Wayne Barrett
Cramer's Rule; the Editors
The Multipliacativity of the Determinant; William Watkins and the Editors

Part 2- Determinants
Introduction; the Editors
The Determinant of a Sum of Matrices; L.M. Weiner
Determinants of Sums; Marvin Marcus
An Application of Determinants; Helen Skala
Cramer's Rule via Selective Annihilation; Dan Kalman
The Multiplication of Determinants; D.C. Lewis
A Short Proof of a Result of Determinants; George Marsaglia
Dodgson's Identity; Wayne Barrett
On the Evaluation of Determinants by Chio's Method; L.E. Fuller and J.D. Logan
Apropos Predetermined Determinants; Antal E. Fekete

Part 3-Eigenanalysis
Introduction- the Editors
Eigenvalues, Eigenvectors and Linear Matrix Equations; Charles R. Johnson
Matrices with "Custom Built" Eigenspaces; W.P. Galvin
A Note on Normal Matrices; C.G. Cullen
Eigenvectors: Fixed Vectors and fixed Directions (Discovery Exercises); J. Stuart
On Cauchy's Inequalities for Hermitian Matrices; Emeric Deutsch and Harry Hochstadt
The Monotonicity Theorem, Cauchy's Interlace Theorem and the Courant-Fisher Theorem; Yasuhiko Ikebe, Toshiyuki Inagaki, and Sadaaki Miyamoto
The Power Method for Finding Eigenvalues on a Microcomputer; Gareth Williams and Donna Williams
Singular values and the Spectral Theorem; K. Hoechsmann
The Characteristic Polynomial of a Singular Matrix; D.E. Varberg
Characteristic Roots or Rank 1 Matrices; Larry Cummings
A Method for Finding the Eigenvectors of a n X n Matrix Corresponding to Eigenvalues of Multiplicity One; M. Carchidi

Part 4- Geometry
Introduction; the Editors
Cram-Schmidt Projections; Charles R. Johnson, D. Olesky, and p. van den Driessche
Pythagoras and the Cauchy-Schwarz Inequality; Ladnor Geissinger
An Application of the Schwarz Inequality; V.G. Sigillito
A Geometric Interpretation of Cramer's Rule; Gregory Conner and Michael Lundquist
Isometries of lp-norm; Chi-Kwong Li and Wasin So
Matrices Which Take a Given Vector into a Given Vector; M. Machover
The Matrix of Rotation; Roger C. Alperin
Standard Least Squares Problem; James Foster
Multigrid Graph Paper; Jean H. Bevis

Part 5- Matrix Forms
Introduction; the Editors
LU Factorization; Charles R. Johnson
Singular Value Decomposition: The 2 X 2 Case; Michael Lundquist
A Simple Proof of the Jordan Decomposition Theorem for Matrices; Israel Goldberg and Seymour Goldberg
Similarity of Matrices; William Watkins
Classifying Row-reduced Echelon Matrices; Stewart Venit and Wayne Bishop

Part 6- Polynomials and Matrices
Introduction; the Editors
On the Cayley-Hamilton Theorem; Robert Reams
On Polynomial Matrix Equations; Harley Flanders
The Matrix Equations X squared=A; W.R. Utz
Where Did the Variables Go?; Stephen Barnett
A Zero-Row Reduction Algorithm for Obtaining the gcd of Polynomials; Sidney H. JKung and Yap S. Chua

Part 7- Linear Systems, Inverses and Rank
Introduction; the Editors
Left and Right Inverses; the Editors
Row and column Ranks Are Always Equal; Dave Stanford
A Proof of the Equality of Column and Row Rank of a Matrix; Hans Liebeck
The Frobenius Rank Inequality; Donald Robinson
A New Algorithm for Computing the Rank of a Matrix; Larry Gerstein
Elementary Row Operations and LU Decomposition; David P. Kraines, Vivian Kraines, and David A. Smith
A Succinct Notation for Linear Combinations of Abstract Vectors; Leon Katz
Why Should We Pivot in Gaussian Elimination?; Edward Rozema
The Gaussian Algorithm for Linear Systems with Interval data; G. Alefeld and G. Mayer
On Sylvester's Law of Nullity; Kurt Bing
Inverses of Vandermonde Matrices; F.D. Parker
On One-sided Inverses of Matrices; Elmar Zemgalis
Integer Matrices Whose Inverses Contain Only Integers; Robert Hanson

Part 8- Applications
Introduction; the Editors
The Matrix-Tree Theorem; Ralph P. Grimaldi and Robert J. Lopez
Algebraic Integers and Tensor Products of Matrices; Shaun M. Fallat
On Regular Markov Chains; Nicholas J. Rose
Integration by Matrix Inversion; William Swartz
Some Explicit Formulas for the Exponential Matrix; T.M. Apostol
Avoiding the Jordan Canonical Form in the Discussion of Linear Systems with Constant Coefficients; E.J. Putzer
The Discrete Analogue of the Putzer Algorithm; Saber Elaydi
The Minimum Length of a Permutation as a Product of Transpositions; George Mackiw

Part 9- Other Topics
Introduction; the Editors
Positive Definite Matrices; C.R. Johnson
Quaternions; Robert S. Smith
Bionomial Matrices; Jay Strum
A Combinatorial Theorem on Circulant Matrices; Dean Clark
An Elementary Approach to the Functional Calculus for Matrices; Yasuhiko Ikebe and Toshiyuki Inagaki

Part 10- Problems
Introduction; the Editors
Partitioned Matrix Multiplication
Determinants
Eigenanalysis
Geometry
Matrix Forms
Matrix Equations
Linear Systems, Inverses, and Rank
Applications
Hermitian Matrices
Magic Squares
Special Matrices
Stochastic Matrices
Trace
Other Topics

Author Index
Further Items of Interest