# mathematica kronecker productkronecker sum

• ### Mathematica_nimingzhe2008

2012-2-20 · Collect poly x y arrange a polynomial as a sum of powers of x y . Collect poly patt h apply h to each final coefficientobtained. FactorTerms expr x pull out factors that do not depend on x. FactorTerms poly . FactorTerms poly x y pull out any overall factorthat does not depend on x y .

• ### tensor productsWhy is the Kronecker sum defined for

2019-3-9 · I define the Kronecker sum as follows A ⊕ B = ( a 11 B ⋯ a 1 n B ⋮ ⋱ ⋮ a m 1 B ⋯ a m n B) This worked for my problems where A and B were row and column vectors respectively. In order to test the general case I took A as an m n matrix and B as an p q matrix where ( m n p q) are randomly selected and I populated

• ### Kranc a Mathematica package to generate numerical codes

2006-6-15 · The diagram in Fig. 1 illustrates the relationships between the Kranc packages KrancThorns TensorTools CodeGen Thorn and MapLookup which are described in the following subsections.Structuring the code in this way separating out the different logically independent functions promotes code reuse. For example none of the thorn generation packages need to know anything

• ### Sums of Kronecker products of elements of one list with

2020-6-14 · The following code generalizes the kronecker products sum and then splits the result. The original code is. lst <- lapply(seq_along(a) function(i) kronecker(a i B i )) res <- Reduce(` ` lst) But following a comment of user G. Grothendieck this can be written as. res <- Reduce(" " Map(kronecker a B)) Then split the results matrix.

• ### Mathematica_nimingzhe2008

2012-2-20 · MathematicaMATHEMATICS AND ALGORITHMSVISUALIZATION AND GRAPHICS . Collect poly x y arrange a polynomial as a sum of powers of x y . FactorTerms poly x y pull out any overall factorthat does not depend on x y . Factor poly

• ### OntheKroneckerProductMathematics

2013-8-1 · OntheKroneckerProduct Kathrin Schacke August 1 2013 Abstract In this paper we review basic properties of the Kronecker product and give an overview of its history and applications.

• ### c#How to compute the Kronecker sum with Ilnumerics

2013-10-2 · 0 2 2 0. It seems that the result in the matrix M is the Kronecker sum of the matrices A and B. The wikipedia article Matrix addition indicates The Kronecker sum is different from the direct sum but is also denoted by ⊕. It is defined using the Kronecker product ⊗ and normal matrix addition. If A is n-by-n B is m-by-m the Kronecker sum is

• ### Kronecker Decomposition New in Mathematica 9

New in Mathematica 9 › Enhanced Control Systems Kronecker Decomposition TransferFunctionModel supports improper transfer functions. When converted to the time domain an improper transfer function creates a descriptor StateSpaceModel.The proper and polynomial parts of the transfer function can be decoupled in the state-space model with KroneckerModelDecomposition.

• ### Simplify sums with Kronecker deltas Online Technical

Hi I am defining a sum using the following code mySum = Sum a i b i i 1 n Then I do myValue = D mySum a k Which naturally gives sum _ i=1 n b(i) delta _ i k . Since no assumptions are made Mathematica can do nothing more to simplify the expression. But then I do Simplify myValue k

• ### Do—Wolfram Language Documentation

Do expr spec first evaluates spec then localizes the variable specified and successively assigns values to it each time evaluating expr. Do effectively uses Block to localize values or variables. Do expr spec 1 spec 2 is effectively equivalent to Do Do expr spec 2 spec 1 .

• ### code golfCalculate the Kronecker sum of two matrices

2016-4-26 · A Kronecker sum has the following properties Ia and Ib are the identity matrices with the dimensions of A and B respectively. A and B are square matrices. Note that A and B can be of different sizes. Given two square matrices A and B calculate the Kronecker sum of the two matrices. The size of the matrices will be at least 2-by-2.

• ### Sequences Sums Series Mathematica Wolfram Language

Sequences Sums Series. In the Wolfram Language integer sequences are represented by lists. Use Table to define a simple sequence Some well-known sequences are built in Define a recursive sequence using RecurrenceTable (Note the use of x min max notation.) Convergent series may be automatically simplified

• ### Sum—Wolfram Language Documentation

Sum f i imin imax j jmin jmax evaluates the multiple sum Sum i = imin imax Sum j = jmin jmax f. Sum f i gives the indefinite sum UnderscriptBox Sum i f.

• ### code golfCalculate the Kronecker sum of two matrices

2016-4-26 · A Kronecker sum has the following properties Ia and Ib are the identity matrices with the dimensions of A and B respectively. A and B are square matrices. Note that A and B can be of different sizes. Given two square matrices A and B calculate the Kronecker sum of the two matrices. The size of the matrices will be at least 2-by-2.

• ### quantum mechanicsKronecker sum or direct sum

2016-1-25 · 1 Answer1. Active Oldest Votes. 4. It is definitely a Kronecker sum. Take the case where there are only two different states and − then for example H = E a † a E − a − † a −. What does a means

• ### Sequences Sums Series Mathematica Wolfram Language

Sequences Sums Series. In the Wolfram Language integer sequences are represented by lists. Use Table to define a simple sequence Some well-known sequences are built in Define a recursive sequence using RecurrenceTable (Note the use of x min max notation.) Convergent series may be automatically simplified

• ### How to decompose a matrix as the sum of Kronecker

2021-7-5 · Stack Exchange network consists of 178 Q A communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers.. Visit Stack Exchange

• ### linear algebraWhy is this sum of Kronecker products

2020-3-22 · M ( n) = 2 ( I 2 ⊗ I n) J 2 ⊗ J n − J 2 ⊗ I n − I 2 ⊗ J n. From here I don t see a way to simplify the expression for M ( n). Of course no formula for the determinant of the sum of two matrices exists so we cannot hope to simplify det M ( n) directly along these lines.

• ### code golfCalculate the Kronecker sum of two matrices

2016-4-26 · A Kronecker sum has the following properties Ia and Ib are the identity matrices with the dimensions of A and B respectively. A and B are square matrices. Note that A and B can be of different sizes. Given two square matrices A and B calculate the Kronecker sum of the two matrices. The size of the matrices will be at least 2-by-2.

• ### c#How to compute the Kronecker sum with Ilnumerics

2013-10-2 · 0 2 2 0. It seems that the result in the matrix M is the Kronecker sum of the matrices A and B. The wikipedia article Matrix addition indicates The Kronecker sum is different from the direct sum but is also denoted by ⊕. It is defined using the Kronecker product ⊗ and normal matrix addition. If A is n-by-n B is m-by-m the Kronecker sum is

• ### Connectedness of Kronecker sum and partial Kronecker row

1984-12-1 · Statistics Probability Letters 2 (1984) 315-317 December 1984 North-Holland CONNECTEDNESS OF KRONECKER SUM AND PARTIAL KRONECKER ROW SUM OF DESIGNS P.N. DANDAWATE G.A. PATWARDHAN and M.N. VARTAK Department of Mathematics Indian Institute of Technology Powai Bombay 400 076 India Received March 1983 Revised July 1984

• ### Kranc a Mathematica package to generate numerical codes

2006-6-15 · Replace the covariant derivative of a sum using the linearity property ∇ a (x y) → ∇ a x ∇ a y. Replace the covariant derivative of an arbitrary expression containing tensorial indices with its expansion in terms of a partial derivative and Christoffel symbols one for each index in the expression e.g. ∇ a V b → ∂ a V b Γ

• ### matrixHow can I compute a Kronecker sum in Mathematica

2021-6-5 · Using the Wikipedia definition of Kronecker sum it seems that we can define it in terms of the Kronecker products which is built in Clear kroneckersum kroneckersum a_ b_ / Dimensions a == Dimensions b = KroneckerProduct a IdentityMatrix Length a KroneckerProduct IdentityMatrix Length b b a = RandomInteger 0 10 5 5 b =

• ### Sums of Kronecker products of elements of one list with

2020-6-14 · The following code generalizes the kronecker products sum and then splits the result. The original code is. lst <- lapply(seq_along(a) function(i) kronecker(a i B i )) res <- Reduce(` ` lst) But following a comment of user G. Grothendieck this can be written as. res <- Reduce(" " Map(kronecker a B)) Then split the results matrix.

• ### KroneckerDelta—Wolfram Language Documentation

gives the Kronecker delta equal to 1 if all the are equal and 0 otherwise. Details KroneckerDelta 0 gives 1 KroneckerDelta n gives 0 for other numeric n .

• ### linear algebraWhy is this sum of Kronecker products

2020-3-22 · M ( n) = 2 ( I 2 ⊗ I n) J 2 ⊗ J n − J 2 ⊗ I n − I 2 ⊗ J n. From here I don t see a way to simplify the expression for M ( n). Of course no formula for the determinant of the sum of two matrices exists so we cannot hope to simplify det M ( n) directly along these lines.

• ### code golfCalculate the Kronecker sum of two matrices

2016-4-26 · A Kronecker sum has the following properties Ia and Ib are the identity matrices with the dimensions of A and B respectively. A and B are square matrices. Note that A and B can be of different sizes. Given two square matrices A and B calculate the Kronecker sum of the two matrices. The size of the matrices will be at least 2-by-2.

• ### kronecker sum mathematicagarcesfruit

Is there an analogue for the sums of Eigenvalues If A is n-by-n B is m-by-m the Kronecker sum is defined by In C# is it possible to calculate the Kronecker sum with Ilnumerics

• ### How to decompose a matrix as the sum of Kronecker

2021-7-5 · Stack Exchange network consists of 178 Q A communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers.. Visit Stack Exchange

• ### LATEX Mathematical SymbolsRice University

2016-5-18 · LATEX Mathematical Symbols The more unusual symbols are not deﬁned in base LATEX (NFSS) and require usepackage amssymb 1 Greek and Hebrew letters β beta λ lambda ρ rho ε varepsilon Γ Gamma Υ Upsilon

• ### kronecker sum mathematicagarcesfruit

Is there an analogue for the sums of Eigenvalues If A is n-by-n B is m-by-m the Kronecker sum is defined by In C# is it possible to calculate the Kronecker sum with Ilnumerics

• ### How to get the result of a multiplication between a matrix

In Mathematica the dot operator is overloaded and can be matrix multiplication matrix-vector multiplication vector-matrix multiplication or the scalar dot product of vectors depending on context. If possible Mathematica also conforms the vectors as needed. For example a nxm matrix can multiply a m-wide row vector without objection.

• ### Chapter 13 Kronecker ProductsSIAM

2006-10-27 · "ajlbook" — 2004/11/9 — 13 36 — page 142 — #150 142 Chapter 13. Kronecker Products decompositions given by P−1AP = J A and Q−1BQ= J B respectively then

• ### Kranc a Mathematica package to generate numerical codes

2006-6-15 · The diagram in Fig. 1 illustrates the relationships between the Kranc packages KrancThorns TensorTools CodeGen Thorn and MapLookup which are described in the following subsections.Structuring the code in this way separating out the different logically independent functions promotes code reuse. For example none of the thorn generation packages need to know anything

• ### quantum mechanicsKronecker sum or direct sum

2016-1-25 · 1 Answer1. Active Oldest Votes. 4. It is definitely a Kronecker sum. Take the case where there are only two different states and − then for example H = E a † a E − a − † a −. What does a means

• ### Simplify sum of Kronecker deltaMathematica Stack Exchange

2021-6-6 · Assume each summation is over all possible values of an index. Assume the two indices of each Kronecker delta have the same domain. Simplify Kronecker delta sum test = Sum A j k l KroneckerDelta j a KroneckerDelta k b B j k l m A j k m KroneckerDelta l c KroneckerDelta j a KroneckerDelta k b B j k l m j

• ### Mathematica_nimingzhe2008

2012-2-20 · MathematicaMATHEMATICS AND ALGORITHMSVISUALIZATION AND GRAPHICS . Collect poly x y arrange a polynomial as a sum of powers of x y . FactorTerms poly x y pull out any overall factorthat does not depend on x y . Factor poly

• ### Sequences Sums Series Mathematica Wolfram Language

Sequences Sums Series. In the Wolfram Language integer sequences are represented by lists. Use Table to define a simple sequence Some well-known sequences are built in Define a recursive sequence using RecurrenceTable (Note the use of x min max notation.) Convergent series may be automatically simplified

• ### Do—Wolfram Language Documentation

Do expr spec first evaluates spec then localizes the variable specified and successively assigns values to it each time evaluating expr. Do effectively uses Block to localize values or variables. Do expr spec 1 spec 2 is effectively equivalent to Do Do expr spec 2 spec 1 .

• ### The eigenvalues of a specific Kronecker sumMathematics

2020-3-29 · This is similar looking to the Kronecker sum of two matrices begin equation A oplus B = I_m otimes A B otimes I_n end equation The Kronecker sum has the property that it s eigenvalues are the pairwise sums of the spectrums of A and B .