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In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an complex matrix is an matrix obtained by transposing and applying complex conjugation to each entry (the complex conjugate of + being , for real numbers and ).
Overleaf is a collaborative cloud-based LaTeX editor used for writing, editing and publishing scientific documents. [ 1 ] [ 2 ] It partners with a wide range of scientific publishers to provide official journal LaTeX templates, and direct submission links.
The Oberheim Xpander (/ ɛ k s ˈ p æ n d ər /) is an analog synthesizer launched by Oberheim in 1984 and discontinued in 1988. It is essentially a keyboardless, six-voice version of the Matrix-12 (released a year later, in 1985).
Let A be a square n × n matrix with n linearly independent eigenvectors q i (where i = 1, ..., n).Then A can be factored as = where Q is the square n × n matrix whose i th column is the eigenvector q i of A, and Λ is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, Λ ii = λ i.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign.
In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector, where is the row vector transpose of . [1] More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector , where denotes the ...
1. A two-dimensional smoothing filter: [] [] = []2. Another two-dimensional smoothing filter with stronger weight in the middle: [] [] = []3. The Sobel operator, used commonly for edge detection: