Lecture Notes for CSE 275 - Matrix Computation with Yang at UC-Merced (UC Merced)

Notes Information

Material Type:Note 4
Class:CSE 275 - Matrix Computation
Subject:Computer Science & Engineering
University:University of California-Merced
  • Best Approximation
  • Similarities
  • Eigenvectors
  • Interpretation
  • Recognition
  • Decomposition
  • Eigenvalues
  • Their (singular)
  • Homogeneous
  • Correlations
Login / Sign Up to View Document
Preview Page 1Preview Page 2Preview Page 3Preview Page 4Preview Page 5Preview Page 6

Sample Document Text

CSE 275 Matrix Computation Ming-Hsuan Yang Electrical Engineering and Computer Science University of California at Merced Merced, CA 95344 http://faculty.ucmerced.edu/mhyang Lecture 4 1/14 Overview Basic de nition: orthogonality, orthogonal projection, distance between subspaces, matrix inverse Matrix decomposition 2/14 Reading Chapters 2 and 3 of Matrix Computations by Gene Golub and Charles Van Loan 3/14 Orthogonality A set vectors fx1;:::;xng in IRm is orthogonal if x>i xj = 0 when i 6= j, and orthonormal if x>i xj = ij Orthogonal vectors are maximally independent for they point in totally di erent directions Subspace: A collection of subspaces S1;:::;Sp in IRm is mutually orthogonal if x>y = 0 whenever x2Si and y2Sj for i 6= j The orthogonal complement of a subspace S IRm is S? =fy2IRm : y>x = 0 8x2Sg It can be shown that ran(A)? = null(A>) The vectors v1;:::;vk form an orthonormal basis for a subspace S IRm if they are orthonormal and span S 4/14 Orthogonality (cont'd) A...

Related Documents

Particularly Notes
Correlation Matrices Notes
Similarities Notes
Conformable Notes
Interdependencies Notes
Factor Loadings Notes
Singular Points Notes
No Correlation Notes
Combinations Notes
The Independent Exam
Dancis Final Exam Exam
Exact Linear Exam
The Independent Exam
Particularly Notes
Correct Method Exam
Complicated Notes
155, "/var/app/current/tmp/"