Exam 1 (See p:\data\math\hartlaub\linearalgebra\exam1.mtw)

Gram-Schmidt process and QR factorization (See p:\data\math\hartlaub\linearalgebra\gram.mw)

An algorithm for converting any basis into an orthonormal basis.

Representing the change of basis in matrix form leads to the QR-Factorization: M = QR, which is unique.

Orthogonal transformations and orthogonal matrices

A linear transformation T is called orthogonal if it preserves the length of vectors. The matrix used to obtain the orthogonal transformation is called an orthogonal matrix.

Transpose of a matrix

Interchange the rows and columns of a matrix.

Symmetric matrices

A square matrix A is symmetric if the transpose of A is equal to A.

A square matrix A is skew-symmetric if the transpose of A is equal to -A.

Properties of transpose and symmetric matrices.

Least Squares and Data Fitting

Group/Class Exercises

Please read Chapter 5 for class on Thursday.