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In mathematics, a periodic matrix set is a set of square matrices in which each square matrix is of a different size, and such that each cell within each matrix within a set contains data associated with some type of periodic distribution.〔Periodic table#Periodicity of chemical properties〕 ==Construction of a set== A set may be specified to contain a fixed number of matrices and is identified by a set number (''S''''M''), where ''S'' is the set identification number and ''M'' is the number of matrices included in the set. There is no limit to the number of matrices which may be members of a periodic set. Each matrix within a set has an identification number (a) and must contain a "root cell". A root cell must be located at any corner of a matrix. All root cells must be located at the same corner of each matrix within a single set. A diagonal line drawn from a root cell to the opposite corner of the same matrix is a "root diagonal". The periodicity is defined by "partial square rings" (rings) of cells adjoining a root cell on two sides. All cells within the same ring, (even if they are located in a different matrix) have a similar "period". If a matrix contains (n+1)2 cells then the outermost ring contains "2n+1" cells which are all included in the same period. A ring identification number (n) identifies each period. The root cell is also the smallest ring and is identified as; n = 0. Each subsequent ring (1, 2, 3, etc.) has 2n+1 cells (3, 5, 7, etc.). Individual cells contained within a ring are identified by their deviation from the root diagonal. Each cell within a ring is assigned a deviation number (D). All cells intersected by the root diagonal have; D = 0. All cell locations in a column deviation have positive values of D. All cell locations in a row deviation have negative values of D. Any cell within a set will require three numbers for the identification of its location; a is the matrix number n is the ring number D is the deviation number The cell could also have its location identified as; a is the matrix number x is the column number (root cell = 0) y is the row number (root cell = 0) The two locational systems are analogous to Radial (anD) and Cartesian (axy) systems. Generally this article will use the "anD" locational method. The contents of any cell must contain data that is periodic in some manner. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Periodic matrix set」の詳細全文を読む スポンサード リンク
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