Four possible perspectives(ways) to produce matrix multiplications(which give the same result): Ordered Collection of Dot Products (result matrix is built elementwise): Left matrix is rows, right matrix is columns. Each element is the dot product of a corresponding row from the left matrix and the column from the right matrix.Continue Reading
Frenet coordinates are an alternative way to describe a curve in 2D space, this most commonly can be useful while computing displacement of a vehicle’s position on the road or a calculating it’s reference path. The Frenet coordinates is composed of two coordinates. s coordinate – representing distance along theContinue Reading
Hidden states are the unknowns we try to detect or predict. The Hidden states have a relationship amongst themselves called the transition probabilities. Observations are the evidence variables that we have a priori. Observations and states have a relationship between them called the emission probabilities.Continue Reading
A prior probability distribution of an uncertain quantity is the probability distribution that would express one’s beliefs about this quantity before some evidence is taken into account. A prior can be determined from past information, such as previous experiments.Continue Reading
Expresses how likely particular values of statistics or a random variables are for a given set of observations. Indexes the family of joint probability distribution of the random sample evaluated at the given observations.Continue Reading
Quantum mechanics describes the smallest scales of energy levels of atoms/waves and subatomic particles/waves. * Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large macroscopic scale. * Quantum mechanics differs from classical physics in that energy, momentum, angular momentum and other quantitiesContinue Reading
R Squared is the coefficient of determination it normally ranges from 0 to 1, and provides a measure of how well observed outcomes, are replicated by the model. The formula is: Residual(Error) sum of squares (RSS), also known as (SSR) , is the sum of the squares of theContinue Reading
Formula of the line is: xcos(θ ) – ysin(θ ) = d d(distance) = Perpendicular distance from origin(reference point) to a line. θ(angle) = Angle of the perpendicular line makes with the x axis (reference direction). Continue Reading
Representing points in a homogeneous way on a projective plane is done for easier way to write down a coordinate system of a point in infinity, and also it’s very convenient way forming lines from points in algebric formulation. Viewing a point on an image from a distance(1 distance awayContinue Reading
Is the regression line good? We need to check the mean and std of x and the mean and std y. r = ((1/n)(∑xi-x¯)/sx) (∑yi -ȳ)/sy = ((1/n)(∑xi-x¯)/sqrt(xi-x¯/n))(∑yi -ȳ)/sqrt(∑yi -ȳ/n) r= (1/n-1) ∑Zscore(xi)Zscore(yi) [-1,1] is the range/interval of the residual/correlation coefficient when r=-1 or r=1 represent that each point willContinue Reading