finite summation
111Formal power series — In mathematics, formal power series are devices that make it possible to employ much of the analytical machinery of power series in settings that do not have natural notions of convergence. They are also useful, especially in combinatorics, for… …
112Maximum likelihood — In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum likelihood estimation provides estimates for the model s… …
113Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… …
114Modular form — In mathematics, a modular form is a (complex) analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main… …
115Mixture density — In statistics, a mixture density is a probability density function which is a convex combination of other probability density functions.Consider a probability density function p ( x , a ) for a variable x , parameterized by a . That is, for each… …
116Order-disorder — In quantum field theory and statistical mechanics in the thermodynamic limit, a system with a global symmetry can have more than one phase. For parameters where the symmetry is spontaneously broken, the system is said to be ordered. When the… …
117logic, history of — Introduction the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic There was a medieval tradition according to which the Greek philosopher …
118THEOLOGY — Introduction Defined by Richard Hooker, the Renaissance theologian, as the science of things divine, theology (from the Greek word theos, God, and logos, word, doctrine ) is a sustained, rational discourse on god , His nature, His relationship to …
119Tensor — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… …
120Lagrange's identity — In algebra, Lagrange s identity is the identity:iggl( sum {k=1}^n a k^2iggr) iggl(sum {k=1}^n b k^2iggr) iggl(sum {k=1}^n a k b kiggr)^2 = sum {i=1}^{n 1} sum {j=i+1}^n (a i b j a j b i)^2 iggl(= {1 over 2} sum {i=1}^n sum {j=1}^n (a i b j …
