Search results
Results From The WOW.Com Content Network
Owing to the Pythagorean theorem, the diagonal dividing one half of a square equals the radius of a circle whose outermost point is the corner of a golden rectangle added to the square. [1] Thus, a golden rectangle can be constructed with only a straightedge and compass in four steps: Draw a square
is the unit circle in P 2 = is the unit hyperbola in P 2. + + + = gives the Fermat cubic surface in P 3 with 27 lines. The 27 lines in this example are easy to describe explicitly: they are the 9 lines of the form (x : ax : y : by) where a and b are fixed numbers with cube −1, and their 18 conjugates under permutations of coordinates.
Date/Time Thumbnail Dimensions User Comment; current: 14:02, 23 November 2008: 600 × 600 (1 KB): Hohum {{Information |Description={{en|1=Showing that the diagonal measurement of a rectangle is the same as the diameter of a circumscribed circle.}} |Source=Own work by uploader |Author=Hohum |Date=November 2008 |Permission= |other_versions= }}
The complex Schur decomposition reads as follows: if A is an n × n square matrix with complex entries, then A can be expressed as [1] [2] [3] = for some unitary matrix Q (so that the inverse Q −1 is also the conjugate transpose Q* of Q), and some upper triangular matrix U. This is called a Schur form of A.
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 general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Applicable to: square, hermitian, positive definite matrix Decomposition: =, where is upper triangular with real positive diagonal entries Comment: if the matrix is Hermitian and positive semi-definite, then it has a decomposition of the form = if the diagonal entries of are allowed to be zero