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 to my departmental mailbox (Dunham
Labs, 4th floor) by 4 pm each Wednesday.
Weekly Syllabus and Homework
Updated 29 April 2014.
|
Week
|
Date
|
Topics
|
Reading
|
Homework
|
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1
|
Tue 14 Jan
|
History of linear algebra. Classical notion of vector. Vector
spaces. Examples of vector spaces.
|
FIS 1.1, 1.2
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|
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Thu 16 Jan
|
More examples of vector spaces. Subspaces. Review of complex numbers
and fields.
|
FIS 1.2, 1.3, Appendix C, D
|
|
2
|
Tue 21 Jan
|
Linear combinations. Span. Systems
of linear equations. Linear dependence/independence.
|
FIS 1.4, 1.5
|
Problem Set #1
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|
Thu 23 Jan
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Linear dependence/independence.
|
FIS 1.5
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3
|
Tue 28 Jan
|
Basis.
Dimension.
|
FIS 1.6
|
Problem Set #2
|
|
Thu 30 Jan
|
Linear
transformations. Null
space. Range.
|
FIS 2.1
|
|
4
|
Tue 04 Feb
|
Rank-Nullity
Theorem. One-to-one
and onto.
|
FIS 2.1
|
Problem Set #3
|
|
Thu 06 Feb
|
Matrix representation of a linear map.
Composition of linear
transformations. Matrix multiplication.
|
FIS 2.2, 2.3
|
|
5
|
Tue 11 Feb
|
Inverse of a linear transformation.
Isomorphism.
Change of coordinates.
Review.
|
FIS 2.4, 2.5, 2.7
|
Midterm exam 1 review
Review Solutions
|
|
Thu 13 Feb
|
Midterm exam 1
|
|
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6
|
Tue 18 Feb
|
Change of coordinates. Change of coordinate matrix.
Elementary
row and column operations. Elementary matrices.
|
FIS 2.5, 3.1
|
Problem Set #4
|
|
Thu 20 Feb
|
Elementary operations/matrices. Rank
of a matrix.
|
FIS 3.1, 3.2
|
|
7
|
Tue 25 Feb
|
Matrix inverse.
Systems of linear equations.
Gaussian elimination.
|
FIS 3.2, 3.4
|
Problem Set #5
|
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Thu 27 Feb
|
Reduced row echelon form.
|
FIS 3.4
|
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8
|
Tue 04 Mar
|
Homogeneous/inhomogeneous systems. Determinants.
|
FIS 3.3, 4.1, 4.2
|
Problem Set #6
|
|
Thu 06 Mar
|
More determinants.
|
FIS 4.2, 4.3
|
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9
|
Tue 11 Mar
|
Spring Break!
|
|
|
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Thu 13 Mar
|
Spring Break!
|
|
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10
|
Tue 18 Mar
|
Spring Break!
|
|
|
|
Thu 20 Mar
|
Spring Break!
|
|
|
11
|
Tue 25 Mar
|
Cramer's rule. Eigenvalues and eigenvectors. Diagonalizability.
|
FIS 4.3, 5.1
|
Problem Set #7
|
|
Thu 27 Mar
|
Characteristic polynomial.
Multiplicity of eigenvalues. Eigenspaces.
Diagonalization. Test for diagonalizability.
|
FIS 5.2, 5.3
|
|
12
|
Tue 01 Apr
|
Midterm exam 2
|
|
Midterm exam 2 review
Review Solutions
|
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Thu 03 Apr
|
Google PageRank algorithm
|
|
|
13
|
Tue 08 Apr
|
Sick day!
|
FIS 6.1, 6.2
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Problem Set #8
|
|
Thu 10 Apr
|
Inner product spaces. Norms. Orthogonal vectors.
Orthonormal basis.
|
FIS 6.1, 6.2
|
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14
|
Tue 15 Apr
|
Gram-Schmidt orthogonalization process. Orthogonal complements.
|
FIS 6.3
|
Problem Set #9
|
|
Thu 17 Apr
|
Adjoint of a linear transformation. Normal and self-adjoint
operators. Spectral theorem for normal operators.
|
FIS 6.4
|
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15
|
Tue 22 Apr
|
Unitary operators. Orthogonal transformations. Spectral theorem for
self-adjoint operators. Quadratic forms.
|
FIS 6.4, 6.5
|
Problem Set #10
|
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Thu 24 Apr
|
Heisenberg's uncertainty principle.
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|
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16
|
Tue 29 Apr
|
Reading period.
|
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Final Exam Review
Solutions
|
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Thu 01 May
|
Final Exam!
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