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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).
The multiplicative identity of R[x] is the polynomial x 0; that is, x 0 times any polynomial p(x) is just p(x). [2] Also, polynomials can be evaluated by specializing x to a real number. More precisely, for any given real number r, there is a unique unital R-algebra homomorphism ev r : R[x] → R such that ev r (x) = r. Because ev r is unital ...
The former code fragment means "assign y to x, and if the new value of x is not zero, execute the following statement". The latter fragment means " if and only if x is equal to y , execute the following statement".
A square matrix with entries 0, 1 and −1 such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. Anti-diagonal matrix: A square matrix with all entries off the anti-diagonal equal to zero. Anti-Hermitian matrix: Synonym for skew-Hermitian matrix. Anti-symmetric matrix
The homogeneous (with all constant terms equal to zero) underdetermined linear system always has non-trivial solutions (in addition to the trivial solution where all the unknowns are zero). There are an infinity of such solutions, which form a vector space , whose dimension is the difference between the number of unknowns and the rank of the ...
Consider the system of linear equations: L i = 0 for 1 ≤ i ≤ M, and variables X 1, X 2, ..., X N, where each L i is a weighted sum of the X i s. Then X 1 = X 2 = ⋯ = X N = 0 is always a solution. When M < N the system is underdetermined and there are always an infinitude of further solutions.
He developed MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe. [25] This was followed by Fortran code for linear equations in 1971. [25] Before version 1.0, MATLAB "was not a programming language; it was a simple interactive matrix calculator. There were no programs, no toolboxes, no graphics.
In certain cases, algorithms or other methods exist for proving that a given expression is non-zero, or of showing that the problem is undecidable.For example, if x 1, ..., x n are real numbers, then there is an algorithm [2] for deciding whether there are integers a 1, ..., a n such that