Introduction to linear and multilinear algebra and matrix theory. As presented to
engineers and as the subject of much numerical analysis, this subject is Matrix Theory.
To an algebraist or geometer, it is the theory of Vector Spaces. Linear algebra, sometimes
disguised as matrix theory, considers sets and functions which preserve linear structure.
In practice this includes a very wide portion of mathematics; thus linear algebra includes
axiomatic treatments, computational matters, algebraic structures, and even parts of
geometry; moreover, it provides tools used for analyzing differential equations, statistical
processes, and even physical phenomena.
The College Mathematics Journal is produced by the Mathematical Association of
America and contains article accessible to college students.. Each of the following is an
article on linear algebra selected from The College Mathematics Journal. These can
potentially be used as a basis for student projects in linear algebra.
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On Transformations and Matrices, Marc Swadener, 4:3, 1973, 44-51, 4.4
Binomial Matrices, Jay E. Strum, 8:5, 1977, 260-266
Mathematics in Archaeology, Gareth Williams, 13:1, 1982, 56-58, C
Visual Thinking about Rotations and Reflections, Tom Brieske, 15:5,
1984, 406-410, 4.4
Harvesting a Grizzly Bear Population, Michael Caulfield and John Kent
and Daniel McCaffrey, 17:1, 1986, 34-46, 4.6, 9.10
Why Should We Pivot in Gaussian Elimination?, Edward Rozema, 19:1,
1988, 63-72, 4.6
Rotations in Space and Orthogonal Matrices, David P. Kraines, 22:3,
1991, 245-247, C, 4.3, 4.4, 4.5
Number Theory and Linear Algebra: Exact Solutions of Integer Systems,
George Mackiw, 23:1, 1992, 52-58, 9.3
Gems of Exposition in Elementary Linear Algebra, David Carlson and
Charles R. Johnson and David Lay and A. Duane Porter, 23:4, 1992, 299303, 1.2, 4.5, 4.7
A Random Ladder Game: Permutations, Eigenvalues, and Convergence of
Markov Chains, Lester H. Lange and James W. Miller, 23:5, 1992, 373385, 4.5, 9.10
Graphs, Matrices, and Subspaces, Gilbert Strang, 24:1, 1993, 20-28, 3.1,
4.3
Linear Algebra and Affine Planar Transformations, Gerald J. Porter, 24:1,
1993, 47-51, 0.4, 4.4
Iterative Methods in Introductory Linear Algebra, Donald R. LaTorre,
24:1, 1993, 79-88, 4.5, 9.6
How Does the NFL Rate the Passing Ability of Quarterbacks?, Roger W.
Johnson, 24:5, 1993, 451-453, C
The Surveyor's Area Formula, Bart Braden, 17:4, 1986, 326-337, 5.2.6,
5.2.8
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Cramer's Rule via Selective Annihilation, Dan Kalman, 18:2, 1987, 136137, C, 4.3
Convex Coordinates, Probabilities, and the Superposition of States,
J.N.Boyd and P.N.Raychowdhury, 18:3, 1987, 186-194, 9.7
Determinantal Loci, Marvin Marcus, 23:1, 1992, 44-47, C
Roots of Cubics via Determinants, Robert Y. Suen, 25:2, 1994, 115-117,
0.7
Vectors Point Toward Pisa, Richard A. Dean, 2:2, 1971, 28-39, 6.3
Arithmetic Matrices and the Amazing Nine-Card Monte, Dean Clark and
Dilip K. Datta, 24:1, 1993, 52-56
A Geometric Interpretation of the Columns of the (Pseudo)Inverse of A,
Melvin J. Maron and Ghansham M. Manwani, 24:1, 1993, 73-75, C
The Matrix of a Rotation, Roger C. Alperin, 20:3, 1989, 230, C, 8.3
The Linear Transformation Associated with a Graph: Student Research
Project, Irl C. Bivens, 24:1, 1993, 76-78, 3.1, 9.1
Constructing a Map from a Table of Intercity Distances, Richard J.
Pulskamp,
Systems of Linear Differential Equations by Laplace Transform, H.
Guggenheimer, 23:3, 1992, 196-202, 6.2
Approaches to the Formula for the nth Fibonacci Number, Russell Jay
Hendel, 25:2, 1994, 139-142, C, 0.2, 5.4.2, 9.3, 9.5
Connecting the Dots Parametrically: An Alternative to Cubic Splines,
Wilbur J. Hildebrand, 21:3, 1990, 208-215, 5.6.1, 9.6
Some Applications of Elementary Linear Algebra in Combinatorics,
Richard A. Brualdi and Jennifer J. Q. Massey, 24:1, 1993, 10-19, 3.2