- #1

- 11,710

- 1,981

On the following site there are some free class notes, 1). on linear algebra, very brief, and 3). more extensive notes on group theory. There is also a set of notes 2). on the Riemann Roch theorem (these last use complex analysis of one and several variables, and algebraic and differential topology; but linear algebra plays a role in the guise of exact sequences of sheaf cohomology, i.e. what kempf calls "global linear algebra"),

(you are also welcome to the research preprints, mostly about principally polarized abelian varieties.)

http://www.math.uga.edu/~roy/

oh and here are some review questions for linear algebra:

Define a eigenvalue of a square matrix A.

Define an eigenvector of a square matrix A.

If a matrix A has a basis of eigenvectors, what does the new matrix for µA (multiplication by A) look like in that basis?

Explain the geometric meaning of the determinant of a square matrix A.

Give the formula for the determinant of a 2by 2 and a 3by 3 matrix A.

Explain how to find the determinant of any matrix by row reduction.

What is the determinant of a product of two matrices?

What is the determinant of a diagonal matrix?

What is the relation between the determinants of two “similar” matrices?

What is special about the determinant of an invertible matrix?

Define characteristic polynomial of a square matrix.

Tell how to recognize an orthogonally diagonalizable matrix.

Tell how to recognize any diagonalizable matrix.

Describe all length and orientation preserving linear maps of R^3, R^n.

Tell how to recognize the matrix of a reflection in a plane in R^3.

Tell how to recognize a matrix of an orthogonal projection in R^3.

If c is an eigenvalue of A, how do you find the eigenvectors for c?

If A is a diagonalizable matrix, how do you actually find a matrix P such that P^(-1)AP is diagonal?

(you are also welcome to the research preprints, mostly about principally polarized abelian varieties.)

http://www.math.uga.edu/~roy/

oh and here are some review questions for linear algebra:

Define a eigenvalue of a square matrix A.

Define an eigenvector of a square matrix A.

If a matrix A has a basis of eigenvectors, what does the new matrix for µA (multiplication by A) look like in that basis?

Explain the geometric meaning of the determinant of a square matrix A.

Give the formula for the determinant of a 2by 2 and a 3by 3 matrix A.

Explain how to find the determinant of any matrix by row reduction.

What is the determinant of a product of two matrices?

What is the determinant of a diagonal matrix?

What is the relation between the determinants of two “similar” matrices?

What is special about the determinant of an invertible matrix?

Define characteristic polynomial of a square matrix.

Tell how to recognize an orthogonally diagonalizable matrix.

Tell how to recognize any diagonalizable matrix.

Describe all length and orientation preserving linear maps of R^3, R^n.

Tell how to recognize the matrix of a reflection in a plane in R^3.

Tell how to recognize a matrix of an orthogonal projection in R^3.

If c is an eigenvalue of A, how do you find the eigenvectors for c?

If A is a diagonalizable matrix, how do you actually find a matrix P such that P^(-1)AP is diagonal?

Last edited: