Search results
Results from the WOW.Com Content Network
In mathematics, an eigenplane is a two-dimensional invariant subspace in a given vector space.By analogy with the term eigenvector for a vector which, when operated on by a linear operator is another vector which is a scalar multiple of itself, the term eigenplane can be used to describe a two-dimensional plane (a 2-plane), such that the operation of a linear operator on a vector in the 2 ...
For two convex polygons P and Q in the plane with m and n vertices, their Minkowski sum is a convex polygon with at most m + n vertices and may be computed in time O(m + n) by a very simple procedure, which may be informally described as follows. Assume that the edges of a polygon are given and the direction, say, counterclockwise, along the ...
A 2×2 real and symmetric matrix representing a stretching and shearing of the plane. The eigenvectors of the matrix (red lines) are the two special directions such that every point on them will just slide on them. The example here, based on the Mona Lisa, provides a simple illustration. Each point on the painting can be represented as a vector ...
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.
Therefore, in this case, the spread is at most equal to the diameter of the circle, the number 2. The spread of a matrix depends only on the spectrum of the matrix (its multiset of eigenvalues). If a second matrix B {\displaystyle B} of the same size is invertible , then B A B − 1 {\displaystyle BAB^{-1}} has the same spectrum as A ...
The bird flu outbreak has taken concerning turns, with more than 60 human cases confirmed. Experts outlined four signs that the virus is going in the wrong direction.
As a direct consequence of simultaneous triangulizability, the eigenvalues of two commuting complex matrices A, B with their algebraic multiplicities (the multisets of roots of their characteristic polynomials) can be matched up as in such a way that the multiset of eigenvalues of any polynomial (,) in the two matrices is the multiset of the ...
Former Rep. Lee Zeldin, Trump's pick to lead the EPA, made $186,000 from paid op-eds and speeches. Some of those op-eds criticized climate policies and ESG.