In mathematics and physics, Penrose graphical notation or tensor diagram notation is a (usually handwritten) visual depiction of multilinear functions...

distinct pairs of indices may be summed this way. Penrose graphical notation is a diagrammatic notation which replaces the symbols for tensors with shapes...

notation (dance) A diagrammatic notation in mathematical notation In physics: Penrose graphical notation Coxeter–Dynkin diagram A visual programming language...

tensor product, string diagrams are called tensor networks or Penrose graphical notation. This has led to the development of categorical quantum mechanics...

associated names for this idea: Mandel notation, Mandel–Voigt notation and Nye notation are others found. Kelvin notation is a revival by Helbig of old ideas...

These are connected together to form a tensor network similar to Penrose graphical notation. Due to the symmetries of the spiders and the properties of the...

physical cables. The graphical depiction of quantum circuit elements is described using a variant of the Penrose graphical notation.[citation needed] Richard...

\alpha }} Tensor Abstract index notation Bra–ket notation Penrose graphical notation Levi-Civita symbol DeWitt notation This applies only for numerical...

Oliver Penrose FRS FRSE (born 6 June 1929) is a British theoretical physicist. He is the son of the scientist Lionel Penrose and brother of the mathematical...

_{3}}\omega _{\sigma (a)\sigma (b)\sigma (c)}} Penrose graphical notation Einstein notation Index notation Tensor Antisymmetric tensor Raising and lowering...

representations of matrix groups. The diagrammatic notation can thus greatly simplify calculations. Roger Penrose described spin networks in 1971. Spin networks...

mathematical notations are mostly diagrammatic, and so are almost entirely script independent. Examples are Penrose graphical notation and Coxeter–Dynkin...

contrast, a dyad is specifically a dyadic tensor of rank one. Einstein notation This notation is based on the understanding that whenever a multidimensional array...

The Penrose–Lucas argument is a logical argument partially based on Kurt Gödel's first incompleteness theorem. In 1931, Gödel proved that every effectively...

matrix A by producing another matrix, often denoted by AT (among other notations). The transpose of a matrix was introduced in 1858 by the British mathematician...

Vectors to Tensors. Springer. p. 225. ISBN 978-3-540-22887-5. section §7. Penrose, Roger (2007). The Road to Reality. Vintage books. ISBN 978-0-679-77631-4...

The original problem was first solved in 1958 by Roger Penrose using ellipses to form the Penrose unilluminable room. He showed that there exists a room...

Roger Penrose: Moore–Penrose inverse, the most widely known generalization of the inverse matrix in particular linear algebra Penrose graphical notation, a...

Shirley Victoria Penrose Hodgson (born 22 February 1945) is a British geneticist. Hodgson studied at Somerville College, Oxford. She worked as a GP, then...

or no columns, called an empty matrix. The specifics of symbolic matrix notation vary widely, with some prevailing trends. Matrices are commonly written...

Metric tensor Multilinear algebra Multilinear subspace learning Penrose graphical notation Regge calculus Ricci calculus Ricci decomposition Tensor (intrinsic...

fields called a tetrad). In the 1990s, Roger Penrose proposed Penrose graphical notation (tensor diagram notation) as a, usually handwritten, visual depiction...

equal to each other and summed over. In Einstein notation this summation is built into the notation. The result is another tensor with order reduced by...

developing Aitken's diagrams, to become part of the technique of Penrose graphical notation. Also, this relation is extensively used in S-duality theories...

Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory...

also sometimes referred to as the Penrose–Terrell effect, the Terrell–Penrose effect or the Lampa–Terrell–Penrose effect. In 1924 by Anton Lampa discussed...

Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is...

notation and include the abstract nature of the state, such as tensor products and transformation rules. The notation parallels the idea of Penrose graphical...

and. In the context of finite automata see. For emphasis placed on the graphical reasoning of tensor networks, see the introduction. For a system of N...

tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning Multivector Geometric algebra Clifford algebra...