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Let A be a finite-dimensional power-associative algebra, then A is the vector space direct sum A=A_(11)+A_(10)+A_(01)+A_(00), where A_(ij), with i,j=0,1 is the subspace of A ...

The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) = e^(A) (1) = sum_(n=0)^(infty)(A^n)/(n!) (2) = ...

The exponential factorial is defined by the recurrence relation a_n=n^(a_(n-1)), (1) where a_0=1. The first few terms are therefore a_1 = 1 (2) a_2 = 2^1=2 (3) a_3 = ...

A generalization of the Kronecker decomposition theorem which states that every finitely generated Abelian group is isomorphic to the group direct sum of a finite number of ...

An analytic function f on the unit disk is called schlicht if 1. f is one-to-one, 2. f(0)=0, and 3. f^'(0)=1, in which case it is written f in S. Schlicht functions have ...

A non-zero module which is not the direct sum of two of its proper submodules. The negation of indecomposable is, of course, decomposable. An abstract vector space is ...

3 is the only integer which is the sum of the preceding positive integers (1+2=3) and the only number which is the sum of the factorials of the preceding positive integers ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

Apply the 196-algorithm, which consists of taking any positive integer of two digits or more, reversing the digits, and adding to the original number. Now sum the two and ...

The so-called explicit formula psi(x)=x-sum_(rho)(x^rho)/rho-ln(2pi)-1/2ln(1-x^(-2)) gives an explicit relation between prime numbers and Riemann zeta function zeros for x>1 ...