## Linear Algebra

Spring 2014

Syllabus.

The course so far.

Record of assignments.

Solutions distributed in class.

The Greek alphabet.

Some tips on dealing with proofs.

Dot products and the Cauchy-Schwarz Inequality.

Cauchy-Schwarz and Triangle Inequalities (Calc III handout).

Proof of Theorem 1.13 (p. 54).

A proof that matrix multiplication is associative.

Some basic facts about inequalities.

Equivalence relations and partitions.

A proof of Lemma 2.7 (p118).

Classwork: Matrix mult and linear combinations.

p110#13b (ec problem).

Expressing solution sets using linear combinations.

Some consequences of the invariance of the Laplace expansion.

The cross product.

The proof of Theorem 3.7 [det(AB)=det(A)det(B)] (p66).

Classical adjoints and inverses.

One way in which section 3.4 can be applied.

Classwork on eigenvalues and eigenspaces.

Definition of vector space and a page from your calculus text.

The first theorem about abstract vector spaces.

An expanded version of Theorem 4.5 (p. 250).

From "dependent" to "independendent" via MAT 225.

A useful test for linear dependence/independence.

Why the r.r.e.f. is unique.

Some characterizations of linear dependence/independence.

A proof of Theorem 3. 7 [det(AB)=det(A)det(B)]using elementary matrices.

A program to compute determinant by row reduction.

Extra Credit Project (formula for Fibonacci numbers).

Proof of Lemma 4.11 (slightly reworked).

A proof that rref is unique.

The transition matrix between two coordinatizations.

The matrix of a rotation in the plane.

Proof of Theorem 5.8 and explanation why matrix mult. is associative.

A good chapter on induction (from a discrete math text).