Quincunx matrix
Encyclopedia
In mathematics
, the matrix
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, the matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
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is often called the quincunx matrix. It is a 2×2 Hadamard matrixHadamard matrixIn mathematics, an Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal...
, and its rows form the basis of a diagonal square latticeSquare latticeIn mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice. It is one of the five types of two-dimensional lattices as classified by their symmetry groups; its symmetry group is known symbolically as p4m.Two...
consisting of the integer points whose coordinates both have the same parity; this lattice is a two-dimensional analogue of the three-dimensional body-centered cubic latticeCubic crystal systemIn crystallography, the cubic crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals....
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