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Logarithmic norm. In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic norm was independently introduced by Germund Dahlquist [1] and Sergei Lozinskiĭ in 1958, for square matrices.
Observed information. In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the "log-likelihood" (the logarithm of the likelihood function ). It is a sample-based version of the Fisher information .
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.
Iterated logarithm. In computer science, the iterated logarithm of , written log * (usually read " log star "), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to . [1] The simplest formal definition is the result of this recurrence relation :
For n ≥ p the matrix S is invertible with probability 1 if V is invertible. If p = V = 1 then this distribution is a chi-squared distribution with n degrees of freedom. Occurrence. The Wishart distribution arises as the distribution of the sample covariance matrix for a sample from a multivariate normal distribution.
The best known lower bound for matrix-multiplication complexity is Ω(n 2 log(n)), for bounded coefficient arithmetic circuits over the real or complex numbers, and is due to Ran Raz. The exponent ω is defined to be a limit point, in that it is the infimum of the exponent over all matrix multiplication algorithms. It is known that this limit ...
The Matrix is an American cyberpunk [1] media franchise consisting of four feature films, beginning with The Matrix (1999) and continuing with three sequels, The Matrix Reloaded, The Matrix Revolutions (both 2003), and The Matrix Resurrections (2021). The first three films were written and directed by the Wachowskis and produced by Joel Silver.
Positive and zero values have been highlighted. In bioinformatics, the BLOSUM ( BLO cks SU bstitution M atrix) matrix is a substitution matrix used for sequence alignment of proteins. BLOSUM matrices are used to score alignments between evolutionarily divergent protein sequences. They are based on local alignments.