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A simple and explicit formula for the number of Latin squares was published in 1992, but it is still not easily computable due to the exponential increase in the number of terms. This formula for the number L n of n × n Latin squares is =! () (), where B n is the set of all n × n {0, 1}-matrices, σ 0 (A) is the number of zero entries in ...
In mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a vector. Specifically, the vectorization of a m × n matrix A, denoted vec (A), is the mn × 1 column vector obtained by stacking the columns of the matrix A on top of one another: Here ...
Sudoku solving algorithms. A typical Sudoku puzzle. A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box.
The set of quaternions is a 4-dimensional vector space over the real numbers, with as a basis, by the component-wise addition. and the component-wise scalar multiplication. A multiplicative group structure, called the Hamilton product, denoted by juxtaposition, can be defined on the quaternions in the following way:
Therefore, the Fourier transform goes from one space of functions to a different space of functions: functions which have a different domain of definition. In general, ξ must always be taken to be a linear form on the space of its domain, which is to say that the second real line is the dual space of the first real line.
The second method is used when the number of elements in each row is the same and known at the time the program is written. The programmer declares the array to have, say, three columns by writing e.g. elementtype tablename[][3];. One then refers to a particular element of the array by writing tablename[first index][second index]. The compiler ...
The Hough transform is a feature extraction technique used in image analysis, computer vision, pattern recognition, and digital image processing. [1] [2] The purpose of the technique is to find imperfect instances of objects within a certain class of shapes by a voting procedure. This voting procedure is carried out in a parameter space, from ...
Coordinate vector. In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular ordered basis. [1] An easy example may be a position such as (5, 2, 1) in a 3-dimensional Cartesian coordinate system with the basis as the axes of this system.