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| MA 35301 - Linear Algebra II |
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Credit Hours: 3.00. Theoretical background for methods and results that appear in MA 35100. Inner products, orthogonality, and applications including least squares.
3.000 Credit hours Syllabus Available Levels: Undergraduate, Graduate, Professional Schedule Types: Distance Learning, Lecture Offered By: College of Science Department: Mathematics Course Attributes: Upper Division May be offered at any of the following campuses: West Lafayette Learning Outcomes: 1. Perform rigorous proofs using the definitions of vector space, subspace, linear combination of vectors, linear dependence and linear independence, bases and dimension. 2. Perform rigorous proofs using the definitions of linear transformation and the null space and range of a linear transformation. 3. Exhibit a clear understanding of the relationship between composition of linear transformation and matrix multiplication. 4. Understand elementary matrices and their use in describing the solution set of a system of linear equations. 5. Understand that the determinant function on n x n matrices with entries in a field F is a function that may be defined recursively, and may be uniquely defined as an alternating multilinear form which takes the identity matrix to 1. 6. Perform rigorous proofs involving eigenvalues and eigenvectors. 7. Understand and be able to apply conditions for a linear operator on a finite-dimensional vector space to be diagonalizable. 8. Preform calculations with Gram-Schmidt, least squares and related topics. 9. Students should be able to do rigorous proofs involving inner product spaces and related topics. |
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