Isometries of the plane
... a matrix AF it will be an orthogonal matrix, and as such it possesses a lot of nice properties, as is well known from linear algebra. For instance we have that T A−1 F = AF from which it follows that (det AF )2 = det(AF ) det(ATF ) = det(AF ATF ) = det(I) = 1 and so, any orthogonal matrix has determ ...
... a matrix AF it will be an orthogonal matrix, and as such it possesses a lot of nice properties, as is well known from linear algebra. For instance we have that T A−1 F = AF from which it follows that (det AF )2 = det(AF ) det(ATF ) = det(AF ATF ) = det(I) = 1 and so, any orthogonal matrix has determ ...
Matrices
... vectors of your own choosing, composed of at least 3 elements. Practice Problems: Multiplication By the Identity Matrix I earlier asserted that the identity matrix was the matrix equivalent of the number 1 because the result of multiplication of any matrix by its corresponding identity matrix is sim ...
... vectors of your own choosing, composed of at least 3 elements. Practice Problems: Multiplication By the Identity Matrix I earlier asserted that the identity matrix was the matrix equivalent of the number 1 because the result of multiplication of any matrix by its corresponding identity matrix is sim ...
Coloring k-colorable graphs using smaller palletes
... 2. In c) running time may be exponential in k. 3. Randomization makes solution much easier. ...
... 2. In c) running time may be exponential in k. 3. Randomization makes solution much easier. ...
Applications in Astronomy
... The middle block is an m × n matrix of sub-blocks which are each m × m diagonal matrices. Hence, it is very sparse, containing only m2n nonzeros. ...
... The middle block is an m × n matrix of sub-blocks which are each m × m diagonal matrices. Hence, it is very sparse, containing only m2n nonzeros. ...
Non-negative matrix factorization
NMF redirects here. For the bridge convention, see new minor forcing.Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.NMF finds applications in such fields as computer vision, document clustering, chemometrics, audio signal processing and recommender systems.