1
Abstract Vector Spaces and Subspaces
Checks the vector-space axioms and recognizes subspaces of matrix, polynomial, and function spaces.
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AMA1751 · Chapter overview
Vector Spaces
Extends subspace, independence, basis, and dimension from R^n to abstract vector spaces and introduces coordinate changes.
Lessons
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Linear Combinations and Independence in Vector Spaces
Transfers span and linear-independence methods from coordinate vectors to general vector spaces.
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3
Bases and Dimension in Vector Spaces
Finds bases and dimensions of matrix and polynomial subspaces and applies the spanning-set and basis theorems.
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4
Coordinate Vectors and Change of Basis
Computes coordinate vectors and change-of-coordinates matrices between bases of R^n and general vector spaces.
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Linear Algebra · AMA1751