Matches in SemOpenAlex for { <https://semopenalex.org/work/W3022479908> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W3022479908 abstract "In this paper we derive some basic results of circuit theory using `Implicit Linear Algebra' (ILA). This approach has the advantage of simplicity and generality. Implicit linear algebra is outlined in [1]. We denote the space of all vectors on $S$ by $mathcal{F}_S$ and the space containing only the zero vector on $S$ by $mathbf{0}_S.$ The dual $mathcal{V}_S^{perp}$ of a vector space $mathcal{V}_S$ is the collection of all vectors whose dot product with vectors in $mathcal{V}_S$ is zero. The basic operation of ILA is a linking operation ('matched composition`) between vector spaces $mathcal{V}_{SP},mathcal{V}_{PQ}$ (regarded as collections of row vectors on column sets $Scup P, Pcup Q,$ respectively with $S,P,Q$ disjoint) defined by $mathcal{V}_{SP}leftrightarrow mathcal{V}_{PQ}equiv {(f_S,h_Q):((f_S,g_P)in mathcal{V}_{SP}, (g_P,h_Q) in mathcal{V}_{PQ}},$ and another ('skewed composition`) defined by $mathcal{V}_{SP}rightleftharpoons mathcal{V}_{PQ}equiv {(f_S,h_Q):((f_S,g_P)in mathcal{V}_{SP}, (-g_P,h_Q) in mathcal{V}_{PQ}}.$ The basic results of ILA are the Implicit Inversion Theorem (which states that $mathcal{V}_{SP}leftrightarrow(mathcal{V}_{SP}leftrightarrow mathcal{V}_S)= mathcal{V}_S,$ iff $mathcal{V}_{SP}leftrightarrow mathbf{0}_Psubseteq mathcal{V}_Ssubseteq mathcal{V}_{SP}leftrightarrowmathcal{F}_S$) and Implicit Duality Theorem (which states that $(mathcal{V}_{SP}leftrightarrow mathcal{V}_{PQ})^{perp}= (mathcal{V}_{SP}^{perp}rightleftharpoons mathcal{V}_{PQ}^{perp}$). We show that the operations and results of ILA are useful in understanding basic circuit theory. We illustrate this by using ILA to present a generalization of Thevenin-Norton theorem where we compute multiport behaviour using adjoint multiport termination through a gyrator and a very general version of maximum power transfer theorem, which states that the port conditions that appear, during adjoint multiport termination through an ideal transformer, correspond to maximum power transfer." @default.
- W3022479908 created "2020-05-13" @default.
- W3022479908 creator A5029536777 @default.
- W3022479908 date "2020-05-02" @default.
- W3022479908 modified "2023-09-26" @default.
- W3022479908 title "Implicit Linear Algebra and Basic Circuit Theory" @default.
- W3022479908 cites W1511374328 @default.
- W3022479908 cites W1533712308 @default.
- W3022479908 cites W1539230026 @default.
- W3022479908 cites W1595379210 @default.
- W3022479908 cites W1977584218 @default.
- W3022479908 cites W1977878416 @default.
- W3022479908 cites W2001930104 @default.
- W3022479908 cites W2012959686 @default.
- W3022479908 cites W2047129940 @default.
- W3022479908 cites W2068844468 @default.
- W3022479908 cites W2075421479 @default.
- W3022479908 cites W2078817385 @default.
- W3022479908 cites W2096876511 @default.
- W3022479908 cites W2115002719 @default.
- W3022479908 cites W2133321180 @default.
- W3022479908 cites W2146560209 @default.
- W3022479908 cites W2150271386 @default.
- W3022479908 cites W2177207193 @default.
- W3022479908 cites W2324166574 @default.
- W3022479908 cites W2526979058 @default.
- W3022479908 cites W2573019749 @default.
- W3022479908 cites W2738635245 @default.
- W3022479908 cites W2907797282 @default.
- W3022479908 cites W2971043731 @default.
- W3022479908 cites W330372241 @default.
- W3022479908 cites W43919218 @default.
- W3022479908 cites W612917828 @default.
- W3022479908 cites W72377610 @default.
- W3022479908 doi "https://doi.org/10.48550/arxiv.2005.00838" @default.
- W3022479908 hasPublicationYear "2020" @default.
- W3022479908 type Work @default.
- W3022479908 sameAs 3022479908 @default.
- W3022479908 citedByCount "1" @default.
- W3022479908 countsByYear W30224799082021 @default.
- W3022479908 crossrefType "posted-content" @default.
- W3022479908 hasAuthorship W3022479908A5029536777 @default.
- W3022479908 hasBestOaLocation W30224799081 @default.
- W3022479908 hasConcept C114614502 @default.
- W3022479908 hasConcept C118615104 @default.
- W3022479908 hasConcept C121332964 @default.
- W3022479908 hasConcept C13336665 @default.
- W3022479908 hasConcept C136119220 @default.
- W3022479908 hasConcept C138885662 @default.
- W3022479908 hasConcept C176370821 @default.
- W3022479908 hasConcept C202444582 @default.
- W3022479908 hasConcept C2778023678 @default.
- W3022479908 hasConcept C2778572836 @default.
- W3022479908 hasConcept C33923547 @default.
- W3022479908 hasConcept C41895202 @default.
- W3022479908 hasConcept C45340560 @default.
- W3022479908 hasConcept C45633534 @default.
- W3022479908 hasConceptScore W3022479908C114614502 @default.
- W3022479908 hasConceptScore W3022479908C118615104 @default.
- W3022479908 hasConceptScore W3022479908C121332964 @default.
- W3022479908 hasConceptScore W3022479908C13336665 @default.
- W3022479908 hasConceptScore W3022479908C136119220 @default.
- W3022479908 hasConceptScore W3022479908C138885662 @default.
- W3022479908 hasConceptScore W3022479908C176370821 @default.
- W3022479908 hasConceptScore W3022479908C202444582 @default.
- W3022479908 hasConceptScore W3022479908C2778023678 @default.
- W3022479908 hasConceptScore W3022479908C2778572836 @default.
- W3022479908 hasConceptScore W3022479908C33923547 @default.
- W3022479908 hasConceptScore W3022479908C41895202 @default.
- W3022479908 hasConceptScore W3022479908C45340560 @default.
- W3022479908 hasConceptScore W3022479908C45633534 @default.
- W3022479908 hasLocation W30224799081 @default.
- W3022479908 hasOpenAccess W3022479908 @default.
- W3022479908 hasPrimaryLocation W30224799081 @default.
- W3022479908 hasRelatedWork W2047173329 @default.
- W3022479908 hasRelatedWork W2092837495 @default.
- W3022479908 hasRelatedWork W2152478214 @default.
- W3022479908 hasRelatedWork W2162674041 @default.
- W3022479908 hasRelatedWork W2617310522 @default.
- W3022479908 hasRelatedWork W2952352293 @default.
- W3022479908 hasRelatedWork W2963699585 @default.
- W3022479908 hasRelatedWork W3117008194 @default.
- W3022479908 hasRelatedWork W4200200616 @default.
- W3022479908 hasRelatedWork W4226320515 @default.
- W3022479908 isParatext "false" @default.
- W3022479908 isRetracted "false" @default.
- W3022479908 magId "3022479908" @default.
- W3022479908 workType "article" @default.