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An exchange matrix is the simplest anti-diagonal matrix.; Any matrix A satisfying the condition AJ = JA is said to be centrosymmetric.; Any matrix A satisfying the condition AJ = JA T is said to be persymmetric.
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
In other words, vec(A) is the vector obtained by vectorizing A in column-major order. Similarly, vec(A T) is the vector obtaining by vectorizing A in row-major order. The cycles and other properties of this permutation have been heavily studied for in-place matrix transposition algorithms.
COLEX stands for column exchange. Since the beginning of the atomic era , a variety of lithium enrichments methods have been developed (such as chemical exchange, electromagnetic, laser, centrifugal [ 1 ] ) and the COLEX process has been the most extensively implemented method so far.
There is a similar notion of column equivalence, defined by elementary column operations; two matrices are column equivalent if and only if their transpose matrices are row equivalent. Two rectangular matrices that can be converted into one another allowing both elementary row and column operations are called simply equivalent .
The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: […] = [] and [] = […]. The set of all row vectors with n entries in a given field (such as the real numbers ) forms an n -dimensional vector space ; similarly, the set of all column vectors with m entries forms an m ...
permute rows; scale rows by a nonzero scalar; add rows to other rows; permute columns, and; scale columns by a nonzero scalar. Thus, we can perform Gaussian elimination on G. Indeed, this allows us to assume that the generator matrix is in the standard form.
The row space of this matrix is the vector space spanned by the row vectors. The column vectors of a matrix. The column space of this matrix is the vector space spanned by the column vectors. In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column ...