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Julia Set made with desmos.com where c = -0.84 + 0.19i Γ(z) in the complex plane made with desmos 3d Desmos also offers other services: the Scientific Calculator, Four Function Calculator, Matrix Calculator, Geometry Tool, Geometry Calculator, and a 3-dimensional calculator beta.
Using homogeneous coordinates they can be represented by invertible 3 × 3 matrices over K which act on the points of PG(2, K) by y = M x T, where x and y are points in K 3 (vectors) and M is an invertible 3 × 3 matrix over K. Two matrices represent the same projective transformation if one is a constant multiple of the other.
A typical graphing calculator by Texas Instruments. A graphing calculator (also graphics calculator or graphic display calculator) is a handheld computer that is capable of plotting graphs, solving simultaneous equations, and performing other tasks with variables. Most popular graphing calculators are programmable calculators, allowing the user ...
Applicable to: m-by-n matrix A of rank r Decomposition: = where C is an m-by-r full column rank matrix and F is an r-by-n full row rank matrix Comment: The rank factorization can be used to compute the Moore–Penrose pseudoinverse of A, which one can apply to obtain all solutions of the linear system =.
Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
Process. A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L1. Then reflect P′ to its image P′′ on the other side of line L2. If lines L1 and L2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
In mathematics, a matrix ( pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix ...
Lyapunov equation. The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems. [1] [2] In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is. where is a Hermitian matrix and is the conjugate transpose of ...
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