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Random matrix. In probability theory and mathematical physics, a random matrix is a matrix -valued random variable —that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the study of properties of random matrices, often as they become large.
In principle, there can be more than one such code for a given word length, but the term Gray code was first applied to a particular binary code for non-negative integers, the binary-reflected Gray code, or BRGC. Bell Labs researcher George R. Stibitz described such a code in a 1941 patent application, granted in 1943.
The machine will perform the following three steps on any odd number until only one 1 remains: Append 1 to the (right) end of the number in binary (giving 2n + 1); Add this to the original number by binary addition (giving 2n + 1 + n = 3n + 1); Remove all trailing 0 s (that is, repeatedly divide by 2 until the result is odd). Example
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column with all other entries 0. [1] : 26 An n × n permutation matrix can represent a permutation of n elements. Pre- multiplying an n -row matrix M by a permutation matrix P, forming PM, results in ...
The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. [1] [2] [3] It is a divide-and-conquer algorithm that reduces the multiplication of two n -digit numbers to three multiplications of n /2-digit numbers and, by repeating this reduction, to at most single-digit ...
Carry (arithmetic) In elementary arithmetic, a carry is a digit that is transferred from one column of digits to another column of more significant digits. It is part of the standard algorithm to add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written ...
The conversion can be done via the intermediate form of a sequence of numbers d n, d n−1, ..., d 2, d 1, where d i is a non-negative integer less than i (one may omit d 1, as it is always 0, but its presence makes the subsequent conversion to a permutation easier to describe).
For example, squaring the number "1111" yields "1234321", which can be written as "01234321", an 8-digit number being the square of a 4-digit number. This gives "2343" as the "random" number. Repeating this procedure gives "4896" as the next result, and so on. Von Neumann used 10 digit numbers, but the process was the same.