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Let A be a C^*-algebra. An element a in A is called self-adjoint if a^*=a. For example, the real functions of the C^*-algebra of C([a,b]) of continuous complex-valued ...

Let K be a class of topological spaces that is closed under homeomorphism, and let X be a topological space. If X in K and for every Y in K such that X subset= Y, X is a ...

A finitely generated discontinuous group of linear fractional transformations z->(az+b)/(cz+d) acting on a domain in the complex plane. The Apollonian gasket corresponds to a ...

n vectors X_1, X_2, ..., X_n are linearly dependent iff there exist scalars c_1, c_2, ..., c_n, not all zero, such that sum_(i=1)^nc_iX_i=0. (1) If no such scalars exist, ...

A module homomorphism is a map f:M->N between modules over a ring R which preserves both the addition and the multiplication by scalars. In symbols this means that ...

R(X_1,...X_n)=sum_(i=1)^nH(X_i)-H(X_1,...,X_n), where H(x_i) is the entropy and H(X_1,...,X_n) is the joint entropy. Linear redundancy is defined as ...

A set of vectors is maximally linearly independent if including any other vector in the vector space would make it linearly dependent (i.e., if any other vector in the space ...

A bounded linear operator T in B(H) on a Hilbert space H is said to be cyclic if there exists some vector v in H for which the set of orbits ...

A search algorithm of a tree that explores the first child of a node before visiting its siblings. Tarjan (1972) and Hopcroft and Tarjan (1973) showed that depth-first search ...

Given a linear code C of length n and dimension k over the field F, a parity check matrix H of C is a n×(n-k) matrix whose rows generate the orthogonal complement of C, i.e., ...