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Matrices

Matrices

Matrices. CS485/685 Computer Vision Dr. George Bebis. Matrix Operations. Matrix addition/subtraction Matrices must be of same size. Matrix multiplication. m x n. q x p. m x p. Condition: n = q. Identity Matrix. Matrix Transpose. Symmetric Matrices. Example:. Determinants. 2 x 2.

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257 views • 25 slides
Vectors

Vectors

Vectors. CS485/685 Computer Vision Dr. George Bebis. n-dimensional Vector. An n -dimensional vector v is denoted as follows: The transpose v T is denoted as follows:. Vector Normalization. Vector normalization ? unit length vector. Example:. Inner (or dot) product.

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306 views • 19 slides
Vectors

Vectors

Vectors. CS485/685 Computer Vision Dr. George Bebis. n-dimensional Vector. An n -dimensional vector v is denoted as follows: The transpose v T is denoted as follows:. Vector Normalization. Vector normalization ? unit length vector. Example:. Inner (or dot) product.

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194 views • 19 slides
Systems of Linear Equations (see Appendix A.6, Trucco & Verri)

Systems of Linear Equations (see Appendix A.6, Trucco & Verri)

Systems of Linear Equations (see Appendix A.6, Trucco & Verri). CS485/685 Computer Vision Prof. George Bebis. Systems of linear equations. An arbitrary system of m linear equations in n unknowns can be written as:. where:. or. Example (m=n=2):. Solutions of Ax=b (m = n).

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188 views • 17 slides
Singular Value Decomposition (SVD) (see Appendix A.6, Trucco & Verri)

Singular Value Decomposition (SVD) (see Appendix A.6, Trucco & Verri)

Singular Value Decomposition (SVD) (see Appendix A.6, Trucco & Verri). CS485/685 Computer Vision Prof. George Bebis. SVD. Any real m x n matrix A can be decomposed uniquely: U is m x n and column orthonormal (U T U=I) D is n x n and diagonal

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110 views • 10 slides

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