SCMA351 พีชคณิตเชิงเส้น Linear Algebra


ปริภูมิเวกเตอร์ การแปลงเชิงเส้น ค่าลักษณะเฉพาะและเวกเตอร์ลักษณะเฉพาะ รูปแบบบัญญัติ ปริภูมิผลคูณภายใน


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


Course information

Textbooks

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

Additional materials



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