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Given a set of linear equations {a_1x+b_1y+c_1z=d_1; a_2x+b_2y+c_2z=d_2; a_3x+b_3y+c_3z=d_3, (1) consider the determinant D=|a_1 b_1 c_1; a_2 b_2 c_2; a_3 b_3 c_3|. (2) Now ...

The logarithmic derivative of a function f is defined as the derivative of the logarithm of a function. For example, the digamma function is defined as the logarithmic ...

On a Riemannian manifold M, tangent vectors can be moved along a path by parallel transport, which preserves vector addition and scalar multiplication. So a closed loop at a ...

A basis vector in an n-dimensional vector space is one of any chosen set of n vectors in the space forming a vector basis, i.e., having the property that every vector in the ...

A linear transformation x_1^' = a_(11)x_1+a_(12)x_2+a_(13)x_3 (1) x_2^' = a_(21)x_1+a_(22)x_2+a_(23)x_3 (2) x_3^' = a_(31)x_1+a_(32)x_2+a_(33)x_3, (3) is said to be an ...

The application of an apodization function.

A space-filling function.

The improvement of the convergence properties of a series, also called convergence acceleration or accelerated convergence, such that a series reaches its limit to within ...

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...