...as a rule, under summation of operators their symbols are added, and under multiplication they are multiplied, either up to terms which are small in some sense or ex
of multiplication by one of the coordinates $ x _ {j} $
13 KB (1,836 words) - 14:55, 7 June 2020
rings and algebras with an associative multiplication, i.e., sets with
two binary operations, addition $+$ and multiplication $\cdot$, that are
11 KB (1,726 words) - 20:09, 15 December 2020
and multiplication by a scalar $ \lambda \in \mathbf C $,
5 KB (691 words) - 17:46, 4 June 2020
among which the most important ones are the order, the addition and the multiplication. In this connection the basic properties of the absolute value must be pres
a scalar.
4 KB (659 words) - 08:01, 6 June 2020
are defined uniquely up to multiplication by a scalar. For all diagrams corresponding to a partition $ \lambda $
denotes the invariant scalar product in $ U _ \lambda $,
18 KB (2,500 words) - 13:04, 18 February 2022
which satisfies axioms 1)–5) is called the scalar (or inner) product of $ x $
which preserves the linear operations and the scalar product.
31 KB (4,586 words) - 18:43, 13 January 2024
is the operator of scalar multiplication by $ \mu ( h) $.
6 KB (805 words) - 08:11, 6 June 2020
...tive, then $\phi$ is called a non-degenerate Hermitian form or a Hermitian scalar product on $X$.
...where $\a$ is an invertible element of $R$. The determinant regarded up to multiplication by such elements is called the determinant of the Hermitian form or of the
5 KB (831 words) - 17:13, 9 October 2016
...Introducing operations of addition, multiplication and multiplication by a scalar for recognition operators allows one to prove that a recognition algorithm
8 KB (1,189 words) - 13:43, 17 April 2014
Axioms which describe the operation of multiplication of a vector by a number.
Multiplication of a vector $ \mathbf a $
25 KB (3,631 words) - 19:39, 5 June 2020
the operations of addition of tensors and of multiplication of a tensor by a scalar from $ k $
...se operations the corresponding components are added, or multiplied by the scalar. The operation of multiplying tensors of different types is also defined; i
13 KB (1,934 words) - 08:25, 6 June 2020
...by introducing on the tensor product $C_1 \tensor_A C_2$ of $A$-modules a multiplication according to the formula
[[Matrix multiplication]]), of two matrices $A = [ \alpha_{ij} ]$ and $B$ is the matrix
11 KB (1,992 words) - 03:52, 23 July 2018
and multiplication by a scalar are defined [[Pointwise operation|pointwise]] by the formulas
5 KB (903 words) - 21:31, 3 January 2021
...alf-plane, and that of a unitary operator lies on the unit circle). If the scalar product is not of fixed sign, but its index of indefiniteness $ \kappa $
that is left inverse to the multiplication operator $ X \mapsto A X - X A $(
16 KB (2,424 words) - 08:22, 6 June 2020
and if the operations of addition, multiplication by a scalar and the zero section satisfy the natural conditions of analyticity. If $
6 KB (951 words) - 06:45, 22 February 2022
and the dot denotes multiplication of spinor fields by vector fields which correspond to the above $ C $-
has positive scalar curvature, then $ \mathop{\rm ker} D = 0 $(
6 KB (923 words) - 17:42, 6 January 2024
induced by left-multiplication on the first factor of $ G ( K ) \times A $.
with the metric induced by the scalar product on $ V $
7 KB (1,021 words) - 06:29, 30 May 2020
is the anti-commutative algebra with multiplication $ [ x , y ] = xy - yx $
as above, the multiplication $ \star $
22 KB (3,154 words) - 19:10, 26 March 2023
ring. The operations of addition and multiplication defined on $K$ are
$\M_n(K)$. Multiplication of matrices is associative: If $A\in\M_{m,k}(K)$, $B\in\M_{k,n}(K)$ and $C\
18 KB (3,377 words) - 17:54, 2 November 2013
and is commutative and associative. The exterior multiplication of differentials on a Riemann surface is distributive with respect to addit
In general, exterior multiplication of a differential of order $ k $
18 KB (2,560 words) - 19:35, 5 June 2020