Click on any of the [ 11] items below.

These will eventually contain the two Syllabus Segments for Spring 2019 Semester:

Syll1Spring19-LinAlg: The syllabus for the first seven weeks of the course.
1. An overview to the start
• Weeks 1-4: The mechanics of solving equations.
• Introducing the geometry of solutions.
2. Vectors describing the range and domain
• The special case m = n.
• Vector spaces.
• Office Hours.
• Syllabus statements.
• Website.
Syll1Spring19-LinAlg.pdf

Syll2Spring19-LinAlg: The syllabus for the last seven weeks of the course.

1. Vector spaces and subspaces, especially § 4.7
2. Determinants, § 3.1-3.3
3. §5.1–§5.4: Eigenvalues and Eigenvectors or how changing basis can put certain matrices in diagonal form
4. §6.1–§6.3: Inner product, orthoganity, orthogonal projections and maybe the Gram-Schmidt Theorem
5. §7.1–§7.2: Diagonalization of symmetric matrices – quadratic forms and the Spectral Theorem
Syll2Spring19-LinAlg.pdf

SimilarityCanonicalClassEx: Canonical form for a similarity class of a matrix A: R9R9 and eigenvalue λ for which the matrix Nλ = A - λ I9 has the property that its cube is the zero matrix, the range of its square has dimension 2 and its range has dimension 5. SimilarityCanonicalClassEx.pdf

These will eventually contain the separate Problems set assignments for Spring 2019 Semester:

Prob1-2130LinAlg-LinesPlanes: The first problem set: on null space of a row reduced matrix, and the relation between lines and planes in R3.

1. Using reduced row echelon form.
2. Lines contained in a given plane.
Note that both parts of the first problem have notation hints given as footnotes. Prob1-2130LinAlg-LinesPlanes.pdf

Prob2-2130LinAlgLinearTransforms: The 2nd problem set: Extending use of row reduced echelon form, and advanced relating a linear transformation to a matrix.

1. Use a matrix in row reduced form.
2. Relating two bases of a vector space.
Prob2-2130LinAlgLinearTransforms.pdf

Prob3-2130LinAlgBasiscos-Jordan: The 3rd problem set: Comparing bases of functions and the simplest case of non-diagonalizability.

1. Bases of cosine functions.
2. A special normal form even if you can't diagonalize a matrix.
Prob3-2130LinAlgBasiscos-Jordan.pdf

This section will contain the midterm and the final for Spring 2019 Semester:

Midterm2130LinAlg:

1. Range of a matrix
2. Transpose of a matrix
3. A linear transformation
4. Commuting and noncommuting matrices
5. The geometry of the space of solutions
Midterm2130LinAlg.pdf

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.

Class01-23-19Lines-Planes: 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.
Class01-23-19Lines-Planes.pdf

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. Mailchimpsignup.html

LinesCurriculum2019: At every stage in mathematics, lines are important, but that doesn't prepare us for the big jump to parametrized lines in, say, R3, 3-space. It is this parametric line that we expect to get as the solution set for two linear equations in 3 unknowns. LinesCurriculum2019.pdf