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The partition on the right-hand side should be the transpose of the partition on the left-hand side, in the sense that if A is an m-by-n block then E should be an n-by-m block. The statement of the nullity theorem is now that the nullities of the blocks on the right equal the nullities of the blocks on the left (Strang & Nguyen 2004):
A partially balanced incomplete block design with n associate classes (PBIBD(n)) is a block design based on a v-set X with b blocks each of size k and with each element appearing in r blocks, such that there is an association scheme with n classes defined on X where, if elements x and y are ith associates, 1 ≤ i ≤ n, then they are together ...
If A is a set, then the absolute complement of A (or simply the complement of A) is the set of elements not in A (within a larger set that is implicitly defined). In other words, let U be a set that contains all the elements under study; if there is no need to mention U, either because it has been previously specified, or it is obvious and unique, then the absolute complement of A is the ...
The Schur complement is named after Issai Schur [1] who used it to prove Schur's lemma, although it had been used previously. [2] Emilie Virginia Haynsworth was the first to call it the Schur complement. [3] The Schur complement is sometimes referred to as the Feshbach map after a physicist Herman Feshbach. [4]
Complementary architecture interprets the Vitruvian triad for contemporary use, mapping durability (firmitas) against aspects of broader sustainability, utility (utilitas) against altruism and service to society, and individual beauty (venustas) against harmony with broader context, regional identity and spirit of place.
A cDNA library is a combination of cloned cDNA (complementary DNA) fragments inserted into a collection of host cells, which constitute some portion of the transcriptome of the organism and are stored as a "library". cDNA is produced from fully transcribed mRNA found in the nucleus and therefore contains only the expressed genes of an organism.
In the branch of mathematics called functional analysis, a complemented subspace of a topological vector space, is a vector subspace for which there exists some other vector subspace of , called its (topological) complement in , such that is the direct sum in the category of topological vector spaces.
In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory. [1] [2] The complementarity principle holds that certain pairs of complementary properties cannot all be observed or measured simultaneously.