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In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as
Formally, the construction is as follows. [1] Let be a vector space over a field, and let be a subspace of .We define an equivalence relation on by stating that iff .That is, is related to if and only if one can be obtained from the other by adding an element of .
Simplified example of training a neural network in object detection: The network is trained by multiple images that are known to depict starfish and sea urchins, which are correlated with "nodes" that represent visual features. The starfish match with a ringed texture and a star outline, whereas most sea urchins match with a striped texture and ...
With the exceptions of 1, 8 and 144 (F 1 = F 2, F 6 and F 12) every Fibonacci number has a prime factor that is not a factor of any smaller Fibonacci number (Carmichael's theorem). [56] As a result, 8 and 144 (F 6 and F 12) are the only Fibonacci numbers that are the product of other Fibonacci numbers. [57]
the sensitivity index d′ (pronounced "d-prime"), the distance between the mean of the distribution of activity in the system under noise-alone conditions and its distribution under signal-alone conditions, divided by their standard deviation, under the assumption that both these distributions are normal with the same standard deviation.
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between space and time.In Albert Einstein's 1905 paper, On the Electrodynamics of Moving Bodies, the theory is presented as being based on just two postulates: [p 1] [1] [2]
Aristotle describes experiments in optics using a camera obscura in Problems, book 15. The apparatus consisted of a dark chamber with a small aperture that let light in. With it, he saw that whatever shape he made the hole, the sun's image always remained circular.
It can be calculated that, over a sufficiently long period such as 1,000,000 spins, the machine will return an average of $950,000 to its players, who have inserted $1,000,000 during that time. In this (simplified) example, the slot machine is said to pay out 95%. The operator keeps the remaining $50,000.