Topologies on quotient space of matrices via semi‐tensor product
Copyright policy )Topologies on quotient space of matrices via semi‐tensor product
AbstractAn equivalence of matrices via semi‐tensor product (STP) is proposed. Using this equivalence, the quotient space is obtained. Parallel and sequential arrangements of the natural projection on different shapes of matrices lead to the product topology and quotient topology respectively. Then the Frobenious inner product of matrices is extended to equivalence classes, which produces a metric on the quotient space. This metric leads to a metric topology. A comparison for these three topologies is presented. Some topological properties are revealed.
- Chinese Academy of Sciences China (People's Republic of)
- Academy of Mathematics and Systems Science China (People's Republic of)
- University of Chinese Academy of Sciences China (People's Republic of)
- Chinese Academy of Science (中国科学院) China (People's Republic of)
- Chinese Academy of Sciences (中国科学院) China (People's Republic of)
quotient space, semi-tensor product, equivalence class, Optimization and Control (math.OC), metric topology, quotient topology, Multilinear algebra, tensor calculus, FOS: Mathematics, Quotient spaces, decompositions in general topology, Product spaces in general topology, Mathematics - Optimization and Control, product topology
quotient space, semi-tensor product, equivalence class, Optimization and Control (math.OC), metric topology, quotient topology, Multilinear algebra, tensor calculus, FOS: Mathematics, Quotient spaces, decompositions in general topology, Product spaces in general topology, Mathematics - Optimization and Control, product topology
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