Kronecker productMobile communicationsIn this paper, an adaptive algorithm is derived by considering that the beamforming vector can be decomposed as a Kronecker product of two smaller vectors. Such a decomposition leads to a joint optimization problem, which is then solved by using an alternating ...
另外,V \times W表示两个向量空间的Cartesian积(维基链接:Cartesian product)。 为了便于理解,这里举一个简单的例子(来源:Calculate the tensor product of two vectors)。 已知\mathbb{R}^2下的一组标准基为\vec e_1=\left(1, 0\right) ^T,\vec e_2=\left(0, 1\right) ^T,\mathbb{R}^3下的一...
另外,V \times W表示两个向量空间的Cartesian积(维基链接:Cartesian product)。 为了便于理解,这里举一个简单的例子(来源:Calculate the tensor product of two vectors)。 已知\mathbb{R}^2下的一组标准基为\vec e_1=\left(1, 0\right) ^T,\vec e_2=\left(0, 1\right) ^T,\mathbb{R}^3下的一...
Let A = [a1 a2 ⋯ am] be an n× m matrix where aj is the jth column vector of A. Then Vec(A) = (a1′, a2′, ⋯, am′)′ is the nm× 1 vector which transforms matrix A into a vector by stacking all the column vectors in A one underneath the other. The basic relation...
kronecker product(矩阵张量乘)
Kronecker product. Kronecker Products – p. 15/22 Eigenvalues and Eigenvectors The Kronecker product of two vectors u ∈ R p and v ∈ R r is a vector u ⊗v ∈ R pr given by u ⊗v = u T v 1 , . . . , u T v r T Suppose now A ∈ R r,r and B ∈ R s,s and ...
Although the concept is relatively simple, it is often beneficial to see several examples of Kronecker products. Example Define andThen, Example Define andThen, Example Consider the two row vectorsandTheir Kronecker product is Example Consider a row vector and a column vectorThen, we have Example...
Note: In mathematics, the Kronecker product, denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a generalization of the outer product (which is denoted by the same symbol) from vectors to matrices, and gives the matrix of the tensor produ...
scalars | vectors | matrices Input matrices, specified as scalars, vectors, or matrices. If either A or B is sparse, then kron multiplies only nonzero elements and the result is also sparse. Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 |...
KroneckerProducts–p7/22KroneckerProduct De,nition1.Foranypositiveintegersp(q)r(swede)netheKroneckerproductoftwomatricesA∈Rp,qandB∈Rr,sasamatrixC∈Rpr,qs giveninblockformas C=,(Ab1)1Ab1,2···Ab1(sb2)1Ab2,2···Ab2,s..br(1Abr)2···Abr(s),,. ...