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Vector Spaces

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Overview

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This course develops vector-space theory through examples and proofs, covering subspaces, spans, direct sums, dimension, replacement theorems, infinite-dimensional spaces, interpolation, and bases via Zorn’s Lemma.

Syllabus

linear algebra vector space (25 examples).
Subspace.
Not subspace.
Union of subspaces.
Span is a subspace.
Intruder Theorem.
Direct Sum.
Dim Sum.
What is a dimension ?.
Replacement Theorem.
Replacement Theorem Proof.
Infinite dimensions.
Lagrange Interpolation.
Zorn’s Lemma and Basis.

Taught by

Dr Peyam

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