Algebra II – Linear Algebra, Spring 2018

Vector Spaces
No. 01, Thursday, 22nd of February
• Space and Subspaces.	exerc	HW1
No. 02, Thursday, 29th of February
• Four Fundamental Subspaces.	exerc	HW2
No. 03, Thursday, 8th of March
• Linear Independence.	exerc	HW3
No. 04, Thursday, 15th of March
• Basis and Dimension.	exerc	HW4
No. 05, Monday, 19th of March
• Linear Transformations.	exerc	HW5
No. 06, Thursday, 29th of March
• Change of Basis and Similarity.	exerc	HW6
No. 07, Monday, 9th of April
• Invariant Subspaces.	exerc	HW7

1st Midterm, Tuesday 17th of April, Famnit-Galeb-Ru3, 9:30

Norms, Inner Products, and Orthogonality
No. 08, Thursday, 12th of April
• Vector Norms. • Inner-Product Spaces.	exerc	HW8
No. 09, Thursday, 19th of April
• Orthogonal Vectors. • Gram–Schmidt Procedure.	exerc	HW9
No. 10, Thursday, 26th of April
• Complementary Subspaces.	exerc	HW10
No. 11, Thursday, 3th of May
• Orthogonal Decomposition.	exerc	HW11
No. 12, Thursday, 10th of May
• Orthogonal Projection.	exerc	HW12
Eigenvalues and Eigenvectors
No. 13, Thursday, 17th of May
• Elementary Properties of Eigensystems • Generalized Eigenvectors and Nilpotnent Operators	exerc	HW13

2nd Midterm, Friday 25th of May, 17:00

No. 14, Thursday, 24th of May
• Self-Adjoint and Normal Operators	exercises
No. 15, Thursday, 31st of May
• The Spectral Theorem • Characteristic and Minimal Polynomials	exercises

For additional reading I recommend the following books