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Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

A piecewise linear function is a function composed of some number of linear segments defined over an equal number of intervals, usually of equal size. For example, consider ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

Turmites, also called turning machines, are 2-dimensional Turing machines in which the "tape" consists of a grid of spaces that can be written and erased by an active ...

"Aggregate" is an archaic word for infinite sets such as those considered by Georg Cantor. The term is sometimes also used to refer to a finite or infinite set in which ...

An algebraic identity is a mathematical identity involving algebraic functions. Examples include the Euler four-square identity, Fibonacci identity, Lebesgue identity, and ...

A field K is said to be algebraically closed if every polynomial with coefficients in K has a root in K.

An antilinear operator A^~ satisfies the following two properties: A^~[f_1(x)+f_2(x)] = A^~f_1(x)+A^~f_2(x) (1) A^~cf(x) = c^_A^~f(x), (2) where c^_ is the complex conjugate ...

The three circular triangles A^'B^'C^', AB^'C^', A^'BC^', and A^'B^'C obtained by extending the arcs of a circular triangle ABC into complete circles.

The average power of a complex signal f(t) as a function of time t is defined as <f^2(t)>=lim_(T->infty)1/(2T)int_(-T)^T|f(t)|^2dt, where |z| is the complex modulus (Papoulis ...