 Site Statistics  |   Contact  |   About Us       Thursday, October 29, 2020  ~ In Smalltalk ~ Math on Vectors ~ Matrix Manipulation ~ Complex Solutions      A Note On Vectors... A vector is an object in a multidimensional space. It is represented by its components measured on a reference system. A reference system is a series of vectors from which the entire space can be generated. A commonly used mathematical notation for a vector is a lowercase bold letter – v, for example. So, if the set of vectors u1,...,un is a reference system for a space with n dimensions, then any vector of the space can be written as,           v = v1u1 + ··· + vnun, where v1,…,vn are real numbers in the case of a real space. These numbers are called the components of a vector. and Matrices... A matrix is a linear operator over vectors from one space to vectors in another space not necessarily of the same dimension. This means that the application of a matrix on a vector is another vector. Matrix is commonly represented with an uppercase bold letter – M, for example. The application of the matrix M on the vector V is denoted by M • v. The fact that a matrix is a linear operator means that           M • (αu + βv) = αM • u + βM • v, for any matrix M, any vectors u and v, and any numbers α and β.  Math, Analysis,
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EIGENVALUE SOLUTIONS...
Eigen Inverse Iteration
Rayleigh-Quotient Method
Cubic Spline Method

 Applied Mathematical Algorithms A complex number z = x + iy, where... Complex Functions Non-linear system methods... Non Linear Systems Construction of differentiation... Differentiation Consider the function where... Integration
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