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In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one ...
A modular multiplicative inverse of a modulo m can be found by using the extended Euclidean algorithm. The Euclidean algorithm determines the greatest common divisor (gcd) of two integers, say a and m. If a has a multiplicative inverse modulo m, this gcd must be 1. The last of several equations produced by the algorithm may be solved for this gcd.
If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A −1. Matrix inversion is the process of finding the matrix which when multiplied by the original matrix gives the identity matrix. [2] Over a field, a square matrix that is not invertible is called singular or ...
Extended Euclidean algorithm also refers to a very similar algorithm for computing the polynomial greatest common divisor and the coefficients of Bézout's identity of two univariate polynomials. The extended Euclidean algorithm is particularly useful when a and b are coprime. With that provision, x is the modular multiplicative inverse of a ...
The multiplicative inverse (reciprocal) of the square root of two (i.e., the square root of 1 / 2 ) is a widely used constant. = = = = 0.707 106 781 186 547 524 400 844 362 104 849 039 284 835 937 688 47... (sequence A010503 in the OEIS)
Inverse proportionality with product x y = 1 . Two variables are inversely proportional (also called varying inversely , in inverse variation , in inverse proportion ) [ 2 ] if each of the variables is directly proportional to the multiplicative inverse (reciprocal) of the other, or equivalently if their product is a constant. [ 3 ]
Reciprocal polynomial. In algebra, given a polynomial. with coefficients from an arbitrary field, its reciprocal polynomial or reflected polynomial, [1][2] denoted by p∗ or pR, [2][1] is the polynomial [3] That is, the coefficients of p∗ are the coefficients of p in reverse order. Reciprocal polynomials arise naturally in linear algebra as ...
Fast inverse square root, sometimes referred to as Fast InvSqrt () or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in IEEE 754 floating-point format. The algorithm is best known for its implementation in 1999 in Quake III ...