Search results
Results from the WOW.Com Content Network
In mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix.It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a standard choice of basis.
In mathematics, Young's inequality for products is a mathematical inequality about the product of two numbers. [1] The inequality is named after William Henry Young and should not be confused with Young's convolution inequality. Young's inequality for products can be used to prove Hölder's inequality.
Given a partition λ of n, write V λ for the Specht module associated to λ. Then the Kronecker coefficients g λ μν are given by the rule =. One can interpret this on the level of symmetric functions, giving a formula for the Kronecker product of two Schur polynomials:
The Kronecker delta has the so-called sifting property that for : = =. and if the integers are viewed as a measure space, endowed with the counting measure, then this property coincides with the defining property of the Dirac delta function () = (), and in fact Dirac's delta was named after the Kronecker delta because of this analogous property ...
where , is the inner product.Examples of inner products include the real and complex dot product; see the examples in inner product.Every inner product gives rise to a Euclidean norm, called the canonical or induced norm, where the norm of a vector is denoted and defined by ‖ ‖:= , , where , is always a non-negative real number (even if the inner product is complex-valued).
In a paper of 1853, Sylvester introduced the following matrix, which is, up to a permutation of the rows, the Sylvester matrix of p and q, which are both considered as having degree max(m, n). [1] This is thus a 2 max ( n , m ) × 2 max ( n , m ) {\displaystyle 2\max(n,m)\times 2\max(n,m)} -matrix containing max ( n , m ) {\displaystyle \max(n ...
Neither the United States nor China would win a trade war, the Chinese Embassy in Washington said on Monday, after U.S. President-elect Donald Trump threatened to slap an additional 10% tariff on ...
The reverse inequality follows from the same argument as the standard Minkowski, but uses that Holder's inequality is also reversed in this range. Using the Reverse Minkowski, we may prove that power means with p ≤ 1 , {\textstyle p\leq 1,} such as the harmonic mean and the geometric mean are concave.