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Linear algebra for advanced studies
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Module 1
Foundations of Vector Spaces
1
Vector Spaces: Definitions and Axioms
Define vector spaces over real and complex fields and verify the axioms for a given set.
2
Subspaces and Spanning Sets
Identify subspaces and construct the span of a set of vectors.
3
Linear Independence of Vectors
Determine the linear independence or dependence of a set of vectors.
4
Understanding Vector Space Bases
Define and construct a basis for a vector space.
5
Dimension of Vector Spaces and Subspaces
Compute the dimension of a vector space and its subspaces.
6
Solution Sets: Span and Affine Subspaces
Describe the structure of solution sets to linear systems using the concepts of span and affine subspaces.
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Linear Transformations and Matrices