Mortality for 2 × 2 Matrices is NP-hard
... Proof. We adapt the proof from [3] which shows that the identity problem in Z2×2 is NP-hard. The proof in [3] essentially consists of two parts. First, an encoding is shown from the subset sum problem to a problem on words - given a finite set of words, can they be combined in such a way as to reach ...
... Proof. We adapt the proof from [3] which shows that the identity problem in Z2×2 is NP-hard. The proof in [3] essentially consists of two parts. First, an encoding is shown from the subset sum problem to a problem on words - given a finite set of words, can they be combined in such a way as to reach ...
Matrix elements for the Morse potential using ladder operators
... The phase factor appearing in Eq. (34) follows from the choice made in Eq. (32), which coxresponds to the usual convention [ll-121. A different convention was used in Rosen's paper [ 131. The expressions above can be also used to calculate matrix elements for a more general potential through the use ...
... The phase factor appearing in Eq. (34) follows from the choice made in Eq. (32), which coxresponds to the usual convention [ll-121. A different convention was used in Rosen's paper [ 131. The expressions above can be also used to calculate matrix elements for a more general potential through the use ...
SOLUTIONS TO HOMEWORK #3, MATH 54
... Scratch work. The only tricky part is finding a matrix B other than 0 or I3 for which AB = BA. There are two choices of B that some people will see right away. Here’s one way to get to those two answers even if you don’t see them right away. ...
... Scratch work. The only tricky part is finding a matrix B other than 0 or I3 for which AB = BA. There are two choices of B that some people will see right away. Here’s one way to get to those two answers even if you don’t see them right away. ...
Introduction to MATLAB Part 1
... Array Operations • While a complicated matrix might have to be entered by hand, evenly spaced matrices can be entered much more readily. The command ...
... Array Operations • While a complicated matrix might have to be entered by hand, evenly spaced matrices can be entered much more readily. The command ...
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.