Main text
Strang, Gilbert, Introduction to Linear Algebra (Edition: 4) Wellesley-Cambridge Press, 2009 (ISBN: 978-0-9802327-1-4).
Similar references
- Lay, Linear Algebra and its Applications, Pearson.
- Lax, Linear Algebra and its Applications, Wiley-Interscience.
- Leon, Linear Algebra with Applications, Pearson.
More advanced references
- Lang, Linear Algebra, Springer.
- Halmos, Finite-Dimensional Vector Spaces, Springer.
- Gelfand, Lectures on Linear Algebra, Dover.
- Axler, Linear Algebra Done Right, Springer.
You can find these books and other useful references in
the math
library. The main text is on reserve.
Prerequisites
MATH 1110 or equivalent AP credit. Students who plan to major or minor in mathematics or take upper-level math courses should take MATH 2210, 2230, or 2940 rather than MATH 2310.
Topics
Introduction to linear algebra for students who wish to focus on the practical applications of the subject. A wide range of applications are discussed and computer software may be used. The main topics are systems of linear equations, matrices, determinants, vector spaces, orthogonality, and eigenvalues. Typical applications are population models, input/output models, least squares, and difference equations.
The list below describes the main goals for Math 2310. We will cover most but probably not all of these in class.
- Solving Ax = b for square systems by elimination (pivots, multipliers, back substitution, invertibility of A, factorization into A = LU)
- Complete solution to Ax = b (column space containing b, rank of A, nullspace of A and special solutions to Ax = 0 from row reduced R)
- Basis and dimension (bases for the four fundamental subspaces)
- Least squares solutions (closest line by understanding projections)
- Orthogonalization by Gram-Schmidt (factorization into A = QR)
- Properties of determinants (leading to the cofactor formula and the sum over all n! permutations, applications to inverses and volume)
- Eigenvalues and eigenvectors (diagonalizing A, computing powers A^k and matrix exponentials to solve difference and differential equations)
- Symmetric matrices and positive definite matrices (real eigenvalues and orthogonal eigenvectors, tests for x'Ax > 0, applications)
- Linear transformations and change of basis (connected to the Singular Value Decomposition -- orthonormal bases that diagonalize A)
- Linear algebra in engineering (graphs and networks, Markov matrices, Fourier matrix, Fast Fourier Transform, linear programming)
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