Math 225 Linear Algebra and Matrix Theory
The official syllabus in pdf form.
The text Linear Algebra, 4th Edition by Friedberg, Insel, and
Spence will be referred to as FIS.
Weekly problem sets will be due in class on Thursday.
Weekly Syllabus and Homework
Updated April 24, 2015.
Week

Date

Topics

Reading

Homework

1

Tue 13 Jan

History of linear algebra. Classical notion of vector. Vector
spaces. Examples of vector spaces.

FIS 1.1, 1.2


Thu 15 Jan

More examples and basic properties of vector spaces. Review of complex numbers
and fields.

FIS 1.2, Appendix C, D

2

Tue 20 Jan

Subspaces.

FIS 1.3

Problem Set #1

Thu 22 Jan

Linear combinations. Span. Systems
of linear equations.

FIS 1.4

3

Tue 27 Jan

Nor'easter Juno!



Thu 29 Jan

Linear
dependence/independence. Basis.

FIS 1.5, 1.6

4

Tue 03 Feb

Basis.
Dimension.
Linear
transformations.

FIS 1.6, 2.1

Problem Set #2

Thu 05 Feb

Quiz 1.
Linear
transformations. Null
space. Range.
RankNullity
Theorem. Onetoone
and onto.

FIS 2.1

5

Tue 10 Feb

Review of bases.
Coordinate vector. Matrix representation of a linear map.

FIS 2.2

Problem Set #3

Thu 12 Feb

Space of linear maps.
Composition of linear
transformations. Matrix multiplication.

FIS 2.2, 2.3

6

Tue 17 Feb

Left multiplication transformations.
Inverse of a linear transformation.

FIS 2.3, 2.4

Problem Set #4

Thu 19 Feb

Isomorphism.
Change of coordinates.

FIS 2.4, 2.5,

7

Tue 24 Feb

Change of coordinates.
Elementary
row and column operations. Elementary matrices.
Rank
of a matrix.
Matrix inverse.

FIS 2.5, 3.1, 3.2

Problem Set #5

Thu 26 Feb

Gaussian
elimination using row and column operations.

FIS 3.2

8

Tue 03 Mar

Reduced row echelon form.
Homogeneous/inhomogeneous systems.

FIS 3.3, 3.4

Midterm review
Review Solutions

Thu 05 Mar

Midterm exam!


9

Tue 10 Mar

Spring Break!



Thu 12 Mar

Spring Break!


10

Tue 17 Mar

Spring Break!



Thu 19 Mar

Spring Break!


11

Tue 24 Mar

Determinants.

FIS 4.1, 4.2, 4.3

Problem Set #6

Thu 26 Mar

More determinants.
Eigenvalues and eigenvectors.
Diagonalization.

FIS 4.3, 5.1, 5.2

12

Tue 31 Mar

Characteristic polynomial.
Eigenspaces.
Diagonalization.

FIS 5.1, 5.2

Problem Set #7

Thu 02 Apr

Google PageRank algorithm


13

Tue 07 Apr

Google PageRank (revisited). Multiplicity of eigenvalues.

FIS 5.2

Problem Set #8

Thu 09 Apr

Inner product spaces. Norms. Orthogonal vectors.
Orthonormal basis.
Quiz 2.

FIS 6.1, 6.2

14

Tue 14 Apr

GramSchmidt orthogonalization process.

FIS 6.2

Problem Set #9

Thu 15 Apr

Adjoint of a linear transformation. Normal and selfadjoint
operators. Spectral Theorem for normal operators.

FIS 6.3, 6.4

15

Tue 21 Apr

Spectral Theorem for
selfadjoint operators. Quadratic forms.

FIS 6.4

Problem Set #10

Thu 23 Apr

Heisenberg's uncertainty principle.


16

Tue 28 Apr

Reading period.


Final Exam Review
Solutions

Tue 05 May

Final Exam!


