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For example, with a matrix stored in row-major order, the rows of the matrix are contiguous in memory and the columns are discontiguous. If repeated operations need to be performed on the columns, for example in a fast Fourier transform algorithm (e.g. Frigo & Johnson, 2005), transposing the matrix in memory (to make the columns contiguous) may ...
Board representation in computer chess is a data structure in a chess program representing the position on the chessboard and associated game state. [1] Board representation is fundamental to all aspects of a chess program including move generation, the evaluation function, and making and unmaking moves (i.e. search) as well as maintaining the state of the game during play.
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations). [1] The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [2]
In example if , and , are two arbitrary selected elements from the same column q of matrix, then, matrix consists one fours of elements (,,,,,), for which are satisfied the equations , =, and , =,. This property, named “Tr-property” is specific to T r {\displaystyle Tr} matrices.
The conjugate transpose of a matrix with real entries reduces to the transpose of , as the conjugate of a real number is the number itself. The conjugate transpose can be motivated by noting that complex numbers can be usefully represented by 2 × 2 {\displaystyle 2\times 2} real matrices, obeying matrix addition and multiplication: [ 3 ]
For example, the determinant of the complex conjugate of a complex matrix (which is also the determinant of its conjugate transpose) is the complex conjugate of its determinant, and for integer matrices: the reduction modulo of the determinant of such a matrix is equal to the determinant of the matrix reduced modulo (the latter determinant ...
A transposition table is a cache of previously seen positions, and associated evaluations, in a game tree generated by a computer game playing program. If a position recurs via a different sequence of moves, the value of the position is retrieved from the table, avoiding re-searching the game tree below that position.
The simplest cache-oblivious algorithm presented in Frigo et al. is an out-of-place matrix transpose operation (in-place algorithms have also been devised for transposition, but are much more complex for non-square matrices). Given m×n array A and n×m array B, we would like to store the transpose of A in B. The naive solution traverses one ...