Click on any of the
These will eventually contain the two Syllabus Segments for Spring 2019 Semester:
: The syllabus for the first seven weeks of the course.
An overview to the start
Weeks 1-4: The mechanics of solving equations.
Introducing the geometry of solutions.
Vectors describing the range and domain
The special case m = n.
Extra Comments about the Course
The syllabus for the last seven weeks of the course.
Vector spaces and subspaces, especially § 4.7
Determinants, § 3.1-3.3
§5.1–§5.4: Eigenvalues and Eigenvectors or how changing basis can put certain matrices in diagonal form
§6.1–§6.3: Inner product, orthoganity, orthogonal projections and maybe the Gram-Schmidt Theorem
§7.1–§7.2: Diagonalization of symmetric matrices – quadratic forms and the Spectral Theorem
Canonical form for a similarity class of a matrix
and eigenvalue λ for which the matrix
- λ I
has the property that its cube is the zero matrix, the range of its square has dimension 2 and its range has dimension 5.
These will eventually contain the separate Problems set assignments for Spring 2019 Semester:
: The first problem set: on
space of a row reduced matrix, and the relation between lines and planes in
Using reduced row echelon form.
Lines contained in a given plane.
Note that both parts of the first problem have notation hints given as footnotes.
: The 2nd problem set: Extending use of row reduced echelon form, and advanced relating a linear transformation to a matrix.
Use a matrix in row reduced form.
Relating two bases of a vector space.
: The 3rd problem set: Comparing bases of functions and the simplest case of non-diagonalizability.
Bases of cosine functions.
A special normal form even if you can't diagonalize a matrix.
This section will contain the midterm and the final for Spring 2019 Semester:
Range of a matrix
Transpose of a matrix
A linear transformation
Commuting and noncommuting matrices
The geometry of the space of solutions
Chronological list of essential material from e-mails:
It will include comments on the Syllabus, material on interpreting the book, and problems with pages from the book discussed in class. It does not replace material in class which will sometimes – for efficiency – rearrange book material.
: Based on combining the presentation of
Lines in the Curriculum
with material from the book.
What the book is calling a vector.
Matrix multiplication: We have only used it to turn a matrix into a function by using a vector as a 1-column matrix.
Heading toward changing a non-row reduced matrix into reduced echelon form, using the key words: row reduction, span, linear independent vectors.
Extra Course Material:
Linear Algebra 2130 Class list signup:
Click on the URL for the html signup form and fill out the boxes, being sure that you have the correct e-mail in it.
At every stage in mathematics, lines are important, but that doesn't prepare us for the big jump to
lines in, say,
, 3-space. It is this parametric line that we expect to get as the solution set for two linear equations in 3 unknowns.
4 Page presentation:
Education Abroad: The World is your classroom
How you would pay, instead of paying CU tuition.
Prerequisites: Each program has a minimum GPA requirement, ranging from 2.5 to 3.25
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