Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 340: Elementary Matrix and Linear Algebra

Student Body: 

The audience for this course consists mostly of engineering, science and mathematics students who have completed the three-semester calculus sequence. Math majors are advised to take 341 instead.

Background and Goals: 

Math 340 is our standard Linear algebra course for non math majors. Math majors are also allowed to take Math 340 for their requirements, although the more theoretical, proof-based Math 341 is recommended in their case. Math 340 covers the principles of linear algebra and the theory of matrices with an emphasis in understanding the concepts and being able to perform calculations. Some proofs are also introduced in Math 340.


Math 320 for some science and engineering students, Math 375 for Honors students, Math 341 for math majors and students interested in a more theoretical approach.

Subsequent Courses: 


Course Content: 
  • Linear Equations and Matrices
    • Matrix algebra
    • Elementary matrices
    • Row operations
    • Inverses
    • Echelon form
    • Gauss-Jordan elimination
  • Real Vector Spaces
    • Vector space axioms
    • Subspaces
    • Span and linear independence
    • Basis and dimension
    • Rank of a matrix
    • Coordinate vectors
  • Linear Transformations and Matrices
    • Kernel and range
    • Isomorphisms
    • Matrix of a linear transformation
    • Similarity and change of basis
  • Determinants
    • Odd and even permutations
    • Computation by row and column operations
    • Cofactor expansions
    • Cramer's rule
    • Inverses of matrices and nonsingularity via determinants
  • Eigenvalues and Eigenvectors
    • Definitions
    • Diagonalization
    • Symmetric matrices
  • Inner Product Spaces
    • Cauchy-Schwarz inequality
    • Angle between vectors
    • Gram-Schmidt process
3. (N-A)
Math 234 or Math 222 & 240. Closed to students with credit for either Math 341 or Math 375.

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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