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MATLAB (an abbreviation of "MATrix LABoratory" [18]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms , creation of user interfaces , and interfacing with programs written in other languages.
Noting that any identity matrix is a rotation matrix, and that matrix multiplication is associative, we may summarize all these properties by saying that the n × n rotation matrices form a group, which for n > 2 is non-abelian, called a special orthogonal group, and denoted by SO(n), SO(n,R), SO n, or SO n (R), the group of n × n rotation ...
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
The graph of the logistic map + = is the plane curve that plots the relationship between and +, with (or x) on the horizontal axis and + (or f (x)) on the vertical axis. The graph of the logistic map looks like this, except for the case r = 0:
In probability and statistics, the log-logistic distribution (known as the Fisk distribution in economics) is a continuous probability distribution for a non-negative random variable.
Where ẑ is the axis of symmetry and θ is the angle between the position of the observer and the ẑ axis (the zenith angle), the solution for the potential will be (,) = = (+ (+)) (). A l and B l are to be determined according to the boundary condition of each problem.
Plot two points (,) and (,) in the (,) space corresponding to the known stress components on both perpendicular planes and , respectively (Figure 4 and 6), following the chosen sign convention. Draw the diameter of the circle by joining points A {\displaystyle A} and B {\displaystyle B} with a straight line A B ¯ {\displaystyle {\overline {AB}}} .
The function () is defined on the interval [,].For a given , the difference () takes the maximum at ′.Thus, the Legendre transformation of () is () = ′ (′).. In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface problem, [1] is an involutive transformation on real-valued functions that are ...