### 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 .

### 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.

### 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 .

### 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

### 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

### 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 =

### Kronecker s Views on the Foundations of Mathematics

1989-1-1 · Cantor s Philosophical Views 65 40 Spinoza B. Ethik. Leipzig 1972. Karl Weierstraß (1815-1897). Courtesy of Springer-Verlag. Leopold Kronecker (1823-1891) Courtesy of Springer-Verlag Archives Kronecker s Views on the Foundations of Mathematics Harold M. Edwards In the past I have lamented that Kronecker did not publish more about his views on the foundations of mathematics.1 I

### 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.

### 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.

### 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

### Simplify sum expression containing Kronecker delta

I think Mathematica is correct. If you have KroneckerDelta t n tau if you sum to a number N equal to or larger than 7 you will have KroneckerDelta t 0 tau KroneckerDelta t 1 tau KroneckerDelta t 7 tau KroneckerDelta t 8 tau since only KroneckerDelta t 7 tau is 1 and the rest are zero your sum

### 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

### 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

### Matlab kron_u010555688

2014-7-15 · kron C=kron (A B) Am n Bp q Cmp nq kronKronecker Kronecker XYKronecker X11 Y X12 Y X1n YX21 Y X22 Y X2n

### 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

### 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.

### 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.

### 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

### 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

### The Matrix Cookbook

2012-11-15 · B Kronecker product 0 The null matrix. Zero in all entries. I The identity matrix Jij The single-entry matrix 1 at (ij) and zero elsewhere A positive de nite matrix A diagonal matrix Petersen Pedersen The Matrix Cookbook Version November 15 2012 Page 5

### 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

### 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.

### 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

### 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.

### Matlab kron_u010555688

2014-7-15 · MatlabkronKronecker . function K = kron (A B) KRON Kronecker tensor product. KRON (X Y) is the Kronecker tensor product of X and Y. The result is a large matrix formed by taking all possible products between the elements of X and

### 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

### 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 .

### proofEquation for impulse train as sum of complex

2016-11-16 · For n = l N (with integer l) we get. (2) S = 1 N ∑ k = 0 N − 1 1 = 1. For other values of n we can use the formula of the geometric sum to get. (3) S = 1 N 1 − e j 2 π n 1 − e j 2 π n / N = 1 N 1 − 1 1 − e j 2 π n / N = 0. Note that the denominator is not zero when n ≠ l N. Consequently we have.

### Kronecker delta 4 rules you need to know

2021-2-1 · Kronecker delta 4 rules you need to know It is impossible to imagine theoretical physics without the Kronecker delta. You will encounter We omit the sum sign but keep in mind that if two equal indices appear in an expression then we sum over that index. Example In the following scalar product we sum over i 3 i=1 a i b

### 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

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

### 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.

### 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

### 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.

### 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

### 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

### 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.

### 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