Complex planeIn mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-axis, called the imaginary axis, is formed by the imaginary numbers. The complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors.
Uncorrelatedness (probability theory)In probability theory and statistics, two real-valued random variables, , , are said to be uncorrelated if their covariance, , is zero. If two variables are uncorrelated, there is no linear relationship between them. Uncorrelated random variables have a Pearson correlation coefficient, when it exists, of zero, except in the trivial case when either variable has zero variance (is a constant). In this case the correlation is undefined.
Argument (complex analysis)In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in Figure 1. It is a multivalued function operating on the nonzero complex numbers. To define a single-valued function, the principal value of the argument (sometimes denoted Arg z) is used. It is often chosen to be the unique value of the argument that lies within the interval .
Estimation of covariance matricesIn statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix.
MathematicsMathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Complex logarithmIn mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related: A complex logarithm of a nonzero complex number , defined to be any complex number for which . Such a number is denoted by . If is given in polar form as , where and are real numbers with , then is one logarithm of , and all the complex logarithms of are exactly the numbers of the form for integers .
Isle of Man TT Mountain CourseThe Isle of Man TT Mountain Course or TT Course is a street and public rural road circuit located in the Isle of Man, used for motorcycle racing. The motorcycle TT Course is used principally for the Isle of Man TT Races and also the separate event of the Isle of Man Festival of Motorcycling for the Manx Grand Prix and Classic TT Races held in September of each year. The start-line for the Isle of Man TT Mountain Course is located on Glencrutchery Road in the town of Douglas, Isle of Man.
Euclidean vectorIn mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a directed line segment, or graphically as an arrow connecting an initial point A with a terminal point B, and denoted by . A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier".
Power of a testIn statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis () when a specific alternative hypothesis () is true. It is commonly denoted by , and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. Statistical power ranges from 0 to 1, and as the power of a test increases, the probability of making a type II error by wrongly failing to reject the null hypothesis decreases.
Data dredgingData dredging (also known as data snooping or p-hacking) is the misuse of data analysis to find patterns in data that can be presented as statistically significant, thus dramatically increasing and understating the risk of false positives. This is done by performing many statistical tests on the data and only reporting those that come back with significant results.
Complexity classIn computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.
