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Comptometer from the 1920s, with nines' complements marked on each key. The method of complements was used in many mechanical calculators as an alternative to running the gears backwards. For example: Pascal's calculator had two sets of result digits, a black set displaying the normal result and a red set displaying the nines' complement of ...
The Schur complement arises when performing a block Gaussian elimination on the matrix M.In order to eliminate the elements below the block diagonal, one multiplies the matrix M by a block lower triangular matrix on the right as follows: = [] [] [] = [], where I p denotes a p×p identity matrix.
The choice of can matter quite strongly: every complemented vector subspace has algebraic complements that do not complement topologically. Because a linear map between two normed (or Banach ) spaces is bounded if and only if it is continuous , the definition in the categories of normed (resp. Banach ) spaces is the same as in topological ...
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 ...
For a reflexive bilinear form, where (,) = (,) = ,, the left and right complements coincide. This will be the case if B {\displaystyle B} is a symmetric or an alternating form . The definition extends to a bilinear form on a free module over a commutative ring , and to a sesquilinear form extended to include any free module over a commutative ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
a.c. – absolutely continuous. acrd – inverse chord function. ad – adjoint representation (or adjoint action) of a Lie group. adj – adjugate of a matrix. a.e. – almost everywhere. AFSOC - Assume for the sake of contradiction; Ai – Airy function. AL – Action limit. Alt – alternating group (Alt(n) is also written as A n.) A.M ...
The ones' complement of a binary number is the value obtained by inverting (flipping) all the bits in the binary representation of the number. The name "ones' complement" [1] refers to the fact that such an inverted value, if added to the original, would always produce an "all ones" number (the term "complement" refers to such pairs of mutually additive inverse numbers, here in respect to a ...