Linear Algebra 2015

Assistants

Frank de Zeeuw – and others…

If you have any questions, please email Frank.

Syllabus

Here is the course information.

Textbook: Lay, Linear Algebra and its Applications (4th edition)

We will cover the following sections from the book:

Week 1: 1.1, 1.2, 1.3, 1.4; Row reduction, vector and matrix notation, span, parametric vector form.

Week 2: 1.5, (1.6), 1.7, 1.8, 1.9; Homogeneous systems, (applications), linear independence, linear transformations.

Week 3: 1.8, 1.9, 2.1; Linear transformations, matrix multiplication.

Week 4: 2.2, 2.3; Invertible matrices.

Week 5: 2.4, 2.5, (2.6); Block matrices, LU factorization, (Leontief model).

Week 6: 3.1, 3.2, 3.3; Determinants.

Week 7: 4.1, 4.2, 4.3; Vector spaces, subspaces, null spaces, column spaces, bases.

Week 8: 4.3, 4.4, 4.5, 4.6; Bases, coordinate systems, dimension, rank.

Week 9: 4.7, 5.1; Change of basis, eigenvectors and eigenvalues. Practice exam.

Week 10: 5.1, 5.2, 5.3, 5.4; Eigenvectors, eigenvalues, characteristic equation, diagonalization.

Week 11: 5.5, 6.1, 6.2; Complex eigenvalues, inner products, orthogonal bases

Week 12: 6.3, 6.4; Orthogonal projection, Gram-Schmidt, QR factorization

Week 13: 6.5, 7.1; Least-squares, diagonalization of symmetric matrices

Week 14: 7.2; Quadratic forms; Review

 

Time and place

– Lectures:

     – Tuesday: CO2, 13:00-15:00;

     – Thursday: CE3, 14:00-16:00.

– Exercise sessions:

     – Tuesday: CM1104 / CM1105 / CM1106, 15:00-16:00;    

     – Thursday: CM1120 / CM1121, 16:00-17:00.