Exact(3)
In the case of first nearest approximation without orbital overlap, Sn,n-1 and Sn,n+1 are empty matrices.
Empty matrices help dealing with maps involving the zero vector space.
There is no common notation for empty matrices, but most computer algebra systems allow creating and computing with them.
Similar(57)
Form an empty matrix with L rows. 3.
Furthermore,, and are, respectively, set to the empty matrix,and vector.
The data matrix could contain even more data, but we choose to construct a completely filled matrix avoiding statistic methods like Least Square Estimation [14] or other robust methods [15] for filling of empty matrix cells.
(c) Augment the index set and the matrix of chosen bases: Λ t = Λt-1∪{λ t } and Φ t = Φ t - 1 φ λ t, where Φ 0 is an empty matrix.
We start from an empty matrix, with the same dimensions as our real data matrix and with all cells initialized at 0. We iterate until we have a product left to place, i.e. as long as NItemsLeft > 0. At each iteration we randomly extract a position from the set of cells that are still increasable (stored in CLeft and PLeft).
(a) We start from an empty matrix with a set of threshold for columns and rows; (b) at each step we select a pair of column and row index to increment a component; (c) after a sequence of assignments, the columns (rows) with no availability are blocked (grayed); (d) last step where only one pair of column and row is available; (e) the resulting null model.
An empty matrix is a matrix in which the number of rows or columns (or both) is zero.
In some contexts, such as computer algebra programs, it is useful to consider a matrix with no rows or no columns, called an empty matrix.
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