Dimension

* The size of a basis

* Morphing Lemma

** Review of Exchange Lemma

** Proof of the Morphing Lemma

** Morphing from one spanning forest to another

* Dimension

** Row rank and column rank of a matrix

** Geometry

** Dimension and rank in graphs

** Cardinality of a vector space over GF(2)

* Subset-Basis Lemma

** Termination of Grow algorithm

** Every subspace of F^D contains a basis

** Estimating dimension

* Superset-Basis Lemma

* Dimension Lemma

* Rank Theorem

** Proof of lemma: For any matrix A, row rank of A ≤ column rank of A

* Simple authentication revisited

* Direct sum

** Direct Sum: Example

** Properties of direct sum

** Direct Sum

** Complementary subspace

* Linear function invertibility

** Extracting an invertible function

** Extracting an invertible function from linear function f : V −→ W

** Linear function invertibility, revisited

* Rank-Nullity Theorem

* Checksum problem revisited

* Matrix invertibility

** Matrix invertibility examples

** Transpose of invertible matrix is invertible

** More matrix invertibility

* Representations of vector spaces

* Annihilator of a vector space

* Annihilator Theorem

* 
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