Misplaced Pages

Orthomodular lattice: Difference between revisions

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
Browse history interactivelyNext edit →Content deleted Content addedVisualWikitext
Revision as of 18:00, 5 October 2006 editByrgenwulf (talk | contribs)1,234 editsNo edit summary  Revision as of 18:06, 14 May 2007 edit undoClark Mobarry (talk | contribs)21 editsm Use lattice operator notation rather than set notation.Next edit →
Line 1: Line 1:
An '''orthomodular lattice''' is an ] <math>L</math> that satisfies the following condition for all <math>x, y \in L</math>: An '''orthomodular lattice''' is an ] <math>L</math> that satisfies the following condition for all <math>x, y \in L</math>:
:If <math>x \leq y</math> then <math> y = x \cup (y \cap x^\perp)</math> :If <math>x \leq y</math> then <math> y = x \lor (x^\perp \land y)</math>


Lattices of this form are of crucial importance for the study of ], since they are part of the axiomisation of the ] ] of ]. Lattices of this form are of crucial importance for the study of ], since they are part of the axiomisation of the ] ] of ].

Revision as of 18:06, 14 May 2007

An orthomodular lattice is an orthocomplemented lattice L {\displaystyle L} that satisfies the following condition for all x , y ∈ L {\displaystyle x,y\in L} :

If x ≤ y {\displaystyle x\leq y} then y = x ∨ ( x ⊥ ∧ y ) {\displaystyle y=x\lor (x^{\perp }\land y)}

Lattices of this form are of crucial importance for the study of quantum logic, since they are part of the axiomisation of the Hilbert space formulation of quantum mechanics.

Stub icon

This algebra-related article is a stub. You can help Misplaced Pages by expanding it.

Categories: