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The identity matrix is a the simplest nontrivial diagonal matrix, defined such that I(X)=X (1) for all vectors X. An identity matrix may be denoted 1, I, E (the latter being ...

An identity graph, sometimes also known as an asymmetric graph or rigid graph (Albertson and Collins 1996), is a graph possessing a single graph automorphism. The numbers of ...

The identity element of an additive group G, usually denoted 0. In the additive group of vectors, the additive identity is the zero vector 0, in the additive group of ...

Chrystal's identity is the algebraic identity ((b-c)^2+(b+c)^2+2(b^2-c^2))/((b^4-2b^2c^2+c^4)[1/((b-c)^2)+2/(b^2-c^2)+1/((b+c)^2)])=1 given as an exercise by Chrystal (1886).

For P and Q polynomials in n variables, |P·Q|_2^2=sum_(i_1,...,i_n>=0)(|P^((i_1,...,i_n))(D_1,...,D_n)Q(x_1,...,x_n)|_2^2)/(i_1!...i_n!), where D_i=partial/partialx_i, |X|_2 ...

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

F_mF_(n+1)-F_nF_(m+1)=(-1)^nF_(m-n), where F_n is a Fibonacci number.

Lagrange's identity is the algebraic identity (sum_(k=1)^na_kb_k)^2=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2)-sum_(1<=k<j<=n)(a_kb_j-a_jb_k)^2 (1) (Mitrinović 1970, p. 41; Marsden ...

The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map. The identity function is ...

The q-hypergeometric function identity _rphi_s^'[a,qsqrt(a),-qsqrt(a),1/b,1/c,1/d,1/e,1/f; sqrt(a),-sqrt(a),abq,acq,adq,aeq,afq] ...