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The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.
The core functionality of NumPy is its "ndarray", for n-dimensional array, data structure. These arrays are strided views on memory. [9] In contrast to Python's built-in list data structure, these arrays are homogeneously typed: all elements of a single array must be of the same type.
The scalar matrices are the center of the algebra of matrices: that is, they are precisely the matrices that commute with all other square matrices of the same size. [ a ] By contrast, over a field (like the real numbers), a diagonal matrix with all diagonal elements distinct only commutes with diagonal matrices (its centralizer is the set of ...
In mathematics, an anti-diagonal matrix is a square matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner (↗), known as the anti-diagonal (sometimes Harrison diagonal, secondary diagonal, trailing diagonal, minor diagonal, off diagonal or bad diagonal).
For a square N×N matrix A n,m = A(n,m), in-place transposition is easy because all of the cycles have length 1 (the diagonals A n,n) or length 2 (the upper triangle is swapped with the lower triangle). Pseudocode to accomplish this (assuming zero-based array indices) is: for n = 0 to N - 1 for m = n + 1 to N swap A(n,m) with A(m,n)
For a square matrix, the diagonal (or main diagonal or principal diagonal) is the diagonal line of entries running from the top-left corner to the bottom-right corner. [ 1 ] [ 2 ] [ 3 ] For a matrix A {\displaystyle A} with row index specified by i {\displaystyle i} and column index specified by j {\displaystyle j} , these would be entries A i ...
The identity matrix I n of size n is the n-by-n matrix in which all the elements on the main diagonal are equal to 1 and all other elements are equal to 0, for example, = [], = [], = [] It is a square matrix of order n, and also a special kind of diagonal matrix.
In mathematics, a square matrix is said to be diagonally dominant if, for every row of the matrix, the magnitude of the diagonal entry in a row is greater than or equal to the sum of the magnitudes of all the other (off-diagonal) entries in that row.