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, 2018.
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Week
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Date
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Topics
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Reading
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Homework
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1
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Tue 16 Jan
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History of linear algebra. Classical notion of vector. Vector
spaces.
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FIS 1.1, 1.2
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Thu 18 Jan
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Examples and basic properties of vector spaces. Review of fields
(real, complex, finite). Subspaces.
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FIS 1.2, 1.3, Appendix C, D
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2
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Tue 23 Jan
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More subspaces.
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FIS 1.3
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Problem Set #1
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Thu 25 Jan
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Linear combinations. Span. Systems
of linear equations.
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FIS 1.4
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3
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Tue 30 Jan
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Linear
dependence/independence.
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FIS 1.5
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Problem Set #2
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Thu 01 Feb
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Basis.
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FIS 1.5, 1.6
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4
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Tue 06 Feb
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Basis.
Dimension.
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FIS 1.6
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Problem Set #3
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Thu 08 Feb
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Linear
transformations. Null
space. Range.
Rank-Nullity
Theorem.
|
FIS 2.1
|
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5
|
Tue 13 Feb
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Quiz 1.
One-to-one
and onto.
Coordinate vector. Matrix representation of a linear map.
|
FIS 2.2
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Problem Set #4
|
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Thu 15 Feb
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Space of linear maps.
Composition of linear
transformations. Matrix multiplication.
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FIS 2.2, 2.3
|
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6
|
Tue 20 Feb
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Left multiplication transformations.
Inverse of a linear transformation.
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FIS 2.3, 2.4
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Problem Set #5
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Thu 22 Feb
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Isomorphism.
Change of coordinates.
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FIS 2.4, 2.5,
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7
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Tue 27 Feb
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Change of coordinates.
Elementary
row and column operations. Elementary matrices.
Rank
of a matrix.
Matrix inverse.
|
FIS 2.5, 3.1, 3.2
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Problem Set #6
|
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Thu 01 Mar
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Gaussian
elimination using row and column operations.
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FIS 3.2
|
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8
|
Tue 06 Mar
|
Reduced row echelon form.
Homogeneous/inhomogeneous systems.
|
FIS 3.3, 3.4
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Midterm review
Review Solutions
|
|
Thu 08 Mar
|
More reduced row echelon form.
Midterm exam! (7:30 - 9:00 pm, Davies)
|
FIS 4.1, 4.2, 4.3
|
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9
|
Tue 13 Mar
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Spring Break!
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Thu 15 Mar
|
Spring Break!
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10
|
Tue 20 Mar
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Spring Break!
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Thu 22 Mar
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Spring Break!
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11
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Tue 27 Mar
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Determinants.
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FIS 4.1, 4.2, 4.3
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Problem Set #7
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Thu 29 Mar
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More determinants.
Eigenvalues and eigenvectors.
Diagonalization.
|
FIS 4.3, 5.1
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12
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Tue 03 Apr
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Characteristic polynomial.
Eigenspaces.
Diagonalization.
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FIS 5.1, 5.2
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Problem Set #8
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Thu 05 Apr
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Google PageRank algorithm
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|
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13
|
Tue 10 Apr
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Multiplicity of eigenvalues.
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FIS 5.2
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Problem Set #9
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Thu 12 Apr
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Inner product spaces. Norms. Orthogonal vectors.
Orthonormal basis.
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FIS 6.1, 6.2
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14
|
Tue 17 Apr
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Gram-Schmidt orthogonalization process.
|
FIS 6.2
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Problem Set #10
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Thu 19 Apr
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Adjoint of a linear transformation.
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FIS 6.3
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15
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Tue 24 Apr
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Spectral Theorem for normal and
self-adjoint operators. Quadratic forms.
|
FIS 6.4, 6.5
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Problem Set #11
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Thu 26 Apr
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Heisenberg's uncertainty principle.
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16
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Tue 01 May
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Reading period.
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Final Exam Review
Solutions
| |
Thu 03 May
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Reading period
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Sun 06 May
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Final Exam!
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