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In probability theory, a transition-rate matrix (also known as a Q-matrix, [1] intensity matrix, [2] or infinitesimal generator matrix [3]) is an array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states.
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It is also known as a unipolar generator, acyclic generator, disk dynamo, or Faraday disc. The voltage is typically low, on the order of a few volts in the case of small demonstration models, but large research generators can produce hundreds of volts, and some systems have multiple generators in series to produce an even larger voltage. [ 17 ]
Compared to randomly generated LDPC codes, structured LDPC codes—such as the LDPC code used in the DVB-S2 standard—can have simpler and therefore lower-cost hardware—in particular, codes constructed such that the H matrix is a circulant matrix. [30] Yet another way of constructing LDPC codes is to use finite geometries.
By the Rouché–Capelli theorem, the system of equations is inconsistent, meaning it has no solutions, if the rank of the augmented matrix (the coefficient matrix augmented with an additional column consisting of the vector b) is greater than the rank of the coefficient matrix. If, on the other hand, the ranks of these two matrices are equal ...
The parity-check matrix H of a Hamming code is constructed by listing all columns of length m that are pair-wise independent. Thus H is a matrix whose left side is all of the nonzero n-tuples where order of the n-tuples in the columns of matrix does not matter.
Linear codes are usually implemented as systematic error-correcting codes (e.g., Reed-Solomon codes in CDs). Convolutional codes are implemented as either systematic or non-systematic codes. Non-systematic convolutional codes can provide better performance under maximum-likelihood decoding.
60 years after the events of The Matrix Revolutions, Neo is now a video game designer and the creator of a video game series simply known as The Matrix, which uses Neo's previous memories in the plot. Neo is 57 years old in the Matrix program, but 60 years have passed in the real world, making Neo 97 years old.