Here, however, we will also need to use the Matrix Differential Calculus ( Kronecker product and vectorization transformations ).
12.
The Kronecker product of A \ otimes B, where A is an m�n matrix and B is a p�q matrix, is expressed as
13.
The scheme also extends to half-integer spins, = in which case the Kronecker product of with the Dirac spinor, ?", has to be considered.
14.
Besides the ordinary matrix multiplication just described, there exist other less frequently used operations on matrices that can be considered forms of multiplication, such as the Hadamard product and the Kronecker product.
15.
The differences between these are that the Kronecker product is just a tensor product of matrices, with respect to a previously-fixed basis, whereas the tensor product is usually given in its intrinsic definition.
16.
This is somewhat elementary, and perhaps you know this already . but in the special case that all your blocks are scalar multiples of each other, then it is a Kronecker product and you can get the eigenvalues of the big matrix.
17.
I am somewhat familiar with representations and characters of groups, and I know that by taking the Kronecker product of two representations of the same group, one ends up with a character which is the product of the two original characters, but I bumped into " symmetrized Kronecker product ".
18.
I am somewhat familiar with representations and characters of groups, and I know that by taking the Kronecker product of two representations of the same group, one ends up with a character which is the product of the two original characters, but I bumped into " symmetrized Kronecker product ".
19.
Also named for Kronecker are the Kronecker limit formula, Kronecker's congruence, Kronecker delta, Kronecker comb, Kronecker symbol, Kronecker product, Kronecker's method for factorizing polynomials, Kronecker substitution, Kronecker's theorem in number theory, Kronecker's lemma, and Eisenstein Kronecker numbers.
20.
In general, a vibrational mode transforming as ? will couple to an electronic state transforming as ? if the symmetric part of the Kronecker product [ ? ?" ? ] S contains ?, unless ? is a double group representation when the antisymmetric part { ? ?" ? } A is considered instead.
