Invertible matrixIn linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
Eigendecomposition of a matrixIn linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. Eigenvalue, eigenvector and eigenspace A (nonzero) vector v of dimension N is an eigenvector of a square N × N matrix A if it satisfies a linear equation of the form for some scalar λ.
Block matrixIn mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or partition it, into a collection of smaller matrices. Any matrix may be interpreted as a block matrix in one or more ways, with each interpretation defined by how its rows and columns are partitioned.
AutocorrelationAutocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.
Knowledge marketA knowledge market is a mechanism for distributing knowledge resources. There are two views on knowledge and how knowledge markets can function. One view uses a legal construct of intellectual property to make knowledge a typical scarce resource, so the traditional commodity market mechanism can be applied directly to distribute it. An alternative model is based on treating knowledge as a public good and hence encouraging free sharing of knowledge. This is often referred to as attention economy.
Definitions of knowledgeDefinitions of knowledge try to determine the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philosophers, for example, that it constitutes a cognitive success or an epistemic contact with reality and that propositional knowledge involves true belief. Most definitions of knowledge in analytic philosophy focus on propositional knowledge or knowledge-that, as in knowing that Dave is at home, in contrast to knowledge-how (know-how) expressing practical competence.
Covariance matrixIn probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions.
Procedural knowledgeProcedural knowledge (also known as knowing-how, and sometimes referred to as practical knowledge, imperative knowledge, or performative knowledge) is the knowledge exercised in the performance of some task. Unlike descriptive knowledge (also known as declarative knowledge, propositional knowledge or "knowing-that"), which involves knowledge of specific facts or propositions (e.g. "I know that snow is white"), procedural knowledge involves one's ability to do something (e.g. "I know how to change a flat tire").
A priori and a posterioriA priori ("from the earlier") and a posteriori ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. A priori knowledge is independent from any experience. Examples include mathematics, tautologies, and deduction from pure reason. A posteriori knowledge depends on empirical evidence. Examples include most fields of science and aspects of personal knowledge. The terms originate from the analytic methods found in Organon, a collection of works by Aristotle.
Accuracy and precisionAccuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements (observations or readings) are to their true value, while precision is how close the measurements are to each other. In other words, precision is a description of random errors, a measure of statistical variability. Accuracy has two definitions: More commonly, it is a description of only systematic errors, a measure of statistical bias of a given measure of central tendency; low accuracy causes a difference between a result and a true value; ISO calls this trueness.
