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 May 1, 2017.
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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 17 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 19 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 24 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 26 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 31 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 02 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 07 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 09 Feb
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Linear
transformations. Null
space. Range.
Rank-Nullity
Theorem.
|
FIS 2.1
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5
|
Tue 14 Feb
|
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 16 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
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Tue 21 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
Midterm Exam review
Review Solutions
|
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Thu 23 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 28 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 02 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 07 Mar
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Reduced row echelon form.
Homogeneous/inhomogeneous systems.
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FIS 3.3, 3.4
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Thu 09 Mar
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Midterm exam!
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9
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Tue 14 Mar
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Spring Break!
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Thu 16 Mar
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Spring Break!
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10
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Tue 21 Mar
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Spring Break!
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Thu 23 Mar
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Spring Break!
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11
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Tue 28 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 30 Mar
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More determinants.
Cramer's rule.
Eigenvalues and eigenvectors.
Diagonalization.
|
FIS 4.3, 5.1, 5.2
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12
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Tue 04 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 06 Apr
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Google PageRank algorithm
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|
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13
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Tue 11 Apr
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Google PageRank (continued). Multiplicity of eigenvalues.
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FIS 5.2
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Problem Set #9
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Thu 13 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
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Tue 18 Apr
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Gram-Schmidt orthogonalization process.
Quiz 2.
|
FIS 6.2
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Problem Set #10
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Thu 20 Apr
|
Adjoint of a linear transformation. Normal and self-adjoint
operators. Spectral Theorem for normal operators.
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FIS 6.3, 6.4
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15
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Tue 25 Apr
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Spectral Theorem for
self-adjoint operators. Quadratic forms.
|
FIS 6.4, 6.5
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Problem Set #11
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Thu 27 Apr
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Heisenberg's uncertainty principle.
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16
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Tue 02 May
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Reading period.
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Final Exam Review
Solutions
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Thu 04 May
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Reading period
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Sat 06 May
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Final Exam!
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