Search results
Results from the WOW.Com Content Network
A complex symmetric matrix can be 'diagonalized' using a unitary matrix: thus if is a complex symmetric matrix, there is a unitary matrix such that is a real diagonal matrix with non-negative entries.
Young diagram of shape (5, 4, 1), English notation Young diagram of shape (5, 4, 1), French notation. A Young diagram (also called a Ferrers diagram, particularly when represented using dots) is a finite collection of boxes, or cells, arranged in left-justified rows, with the row lengths in non-increasing order.
Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, we may summarize all these properties by saying that the n × n rotation matrices form a group, which for n > 2 is non-abelian, called a special orthogonal group, and denoted by SO(n), SO(n,R), SO n, or SO n (R), the group of n × n rotation ...
Indeed, every symmetric matrix with diagonal entries exclusively 1 and nondiagonal entries in the set {,, …} {} is a Coxeter matrix. The Coxeter matrix can be conveniently encoded by a Coxeter diagram, as per the following rules. The vertices of the graph are labelled by generator subscripts.
Every symmetric group has a one-dimensional representation called the trivial representation, where every element acts as the one by one identity matrix. For n ≥ 2 , there is another irreducible representation of degree 1, called the sign representation or alternating character , which takes a permutation to the one by one matrix with entry ...
The symmetrically normalized Laplacian is a symmetric matrix if and only if the adjacency matrix A is symmetric and the diagonal entries of D are nonnegative, in which case we can use the term the symmetric normalized Laplacian. The symmetric normalized Laplacian matrix can be also written as
The symmetric group on a set of size n is the Galois group of the general polynomial of degree n and plays an important role in Galois theory. In invariant theory, the symmetric group acts on the variables of a multi-variate function, and the functions left invariant are the so-called symmetric functions.
In mathematics, the special unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1.. The matrices of the more general unitary group may have complex determinants with absolute value 1, rather than real 1 in the special case.