Search results
Results From The WOW.Com Content Network
Sets of representatives of matrix conjugacy classes for Jordan normal form or rational canonical forms in general do not constitute linear or affine subspaces in the ambient matrix spaces. Vladimir Arnold posed [ 16 ] a problem: Find a canonical form of matrices over a field for which the set of representatives of matrix conjugacy classes is a ...
A canonical form is a labeled graph Canon(G) that is isomorphic to G, such that every graph that is isomorphic to G has the same canonical form as G. Thus, from a solution to the graph canonization problem, one could also solve the problem of graph isomorphism : to test whether two graphs G and H are isomorphic, compute their canonical forms ...
A matrix normal form or matrix canonical form describes the transformation of a matrix to another with special properties. Pages in category "Matrix normal forms" The following 10 pages are in this category, out of 10 total.
This (n 1 + ⋯ + n r) × (n 1 + ⋯ + n r) square matrix, consisting of r diagonal blocks, can be compactly indicated as ,, or (,, …,,), where the i-th Jordan block is J λ i,n i. For example, the matrix = [] is a 10 × 10 Jordan matrix with a 3 × 3 block with eigenvalue 0, two 2 × 2 blocks with eigenvalue the imaginary unit i, and a 3 × ...
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form , [1] minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF ), maxterm canonical form , or Product of Sums ( PoS or POS ) which is a ...
Rather, the Jordan canonical form of () contains one Jordan block for each distinct root; if the multiplicity of the root is m, then the block is an m × m matrix with on the diagonal and 1 in the entries just above the diagonal. in this case, V becomes a confluent Vandermonde matrix. [2]
Eduard Weyr (June 22, 1852 – July 23, 1903) was a Czech mathematician now chiefly remembered as the discoverer of a certain canonical form for square matrices over algebraically closed fields. [1] [2] Weyr presented this form briefly in a paper published in 1885. [3] He followed it up with a more elaborate treatment in a paper published in ...
In mathematics, in linear algebra, a Weyr canonical form (or, Weyr form or Weyr matrix) is a square matrix which (in some sense) induces "nice" properties with matrices it commutes with. It also has a particularly simple structure and the conditions for possessing a Weyr form are fairly weak, making it a suitable tool for studying classes of ...