Lecture2.pdf

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Department
Mathematics
Course
MATB24H3
Professor
Sophie Chrysostomou
Semester
Winter

Description
UniversityofTorontoatScarboroughDepartmentofComputerMathematicalSciencesMATB24SFall2011Lecture21VectorSpacesoverFieldsdefinition11SupposeFisaeldwithidentityelementeandzeroelementzthenthesetViscalledavectorspaceovertheeldFif1Visanonemptysetofobjectscalledvectors2ThereisabinaryoperationcalledadditionanddenotedbybetweenthevectorsinVsuchthatifvwVthenvwV3ThereisascalarmultiplicationdenedbetweenthevectorsinVandthescalarelementsofFsuchthatifvisanyvectorinVandrisanyelementofFthenrvVInadditionthefollowingpropertiesmustbesatisedForallvuwVandallrsFA1vuwvuwAssociativityofadditionA2vuuvCommutativityofadditionA3zVsuchthatzxxforallxVExistanceofadditiveidentityA4ForeachxVxVsuchthatxxzExistanceofadditiveinverseforeachelementofVS1rvurvruDistributivelawS2rsvrvsvDistributivelawS3rsvrsvAssociativelawS4exxforallxVPreservationofscale1
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