## SCMA351 พีชคณิตเชิงเส้น Linear Algebra

ปริภูมิเวกเตอร์ การแปลงเชิงเส้น ค่าลักษณะเฉพาะและเวกเตอร์ลักษณะเฉพาะ รูปแบบบัญญัติ ปริภูมิผลคูณภายใน

Vector spaces; linear transformations; eigenvalues and eigenvectors; canonical forms; inner product spaces.

### Course information

• Instructor
• Krikamol Muandet (Dr. rer nat.)
• E-mail : krikamol-at-gmail.com
• Date/Time
• Every Tuesday 13:00-16:00 (room M304)
• Prerequisites
• None
• Course syllabus

### Textbooks

• Howard Anton and Chris Rorres, Elementary Linear Algebra with Applications, John Wiley & Son, Inc., 1991.
• John B. Fraleigh and Raymond A. Beauregard, Linear Algebra, Addison-Wesley Publishing Company, 1990.
• David Poole, Linear Algebra: A Modern Introduction, Thomson Higher Education, 2006.
• Stephen H. Friedberg, Arnold J. Insel and Lawrence E. Spence, Linear Algebra, Prentice-Hall, Inc., 1989.

### Lectures

 A System of Linear Equations Cramer's rule Row echelon form Gauss-Jordan elimination method Reading : Ref#1, Ref#2, Ref#3 Materials Vector Spaces Subspaces Span and linear independence Column, row, and null spaces Basis and dimension Rank Reading : Ref#1, Ref#2, Ref #3, Ref#4 Materials Homework 1 Inner Product Spaces Inner product Norm Angle and orthogonality Gram–Schmidt Orthonormal basis Reading : Ref#1, Ref#2, Ref#3 Eigenvalues and Eigenvectors Characteristic equation Similarity Diagonalization Reading : Ref#1 Homework 2 Linear Transformation Range and kernel One-to-one and onto transformations Isomorphism Compositions of linear transformation Inverse transformation Reading : Ref#1, Ref#2, Ref#3, Ref#4 Homework 3 Change of Basis Coordinate system Coordinate transformation Linear operators Reading : Ref#1, Ref#2 Applications