8
... 4. There is a zero vector ~0 in V such that ~u + ~0 = ~u. 5. For each ~u in V , there is a vector −~u in V such that ~u + (−~u) = ~0. 6. The scalar multiple c~u is in V . 7. c(~u + ~v ) = c~u + c~v . 8. (c + d)~u = c~u + d~u. 9. c(d~u) = (cd)~u. 10. 1~u = ~u. ...
... 4. There is a zero vector ~0 in V such that ~u + ~0 = ~u. 5. For each ~u in V , there is a vector −~u in V such that ~u + (−~u) = ~0. 6. The scalar multiple c~u is in V . 7. c(~u + ~v ) = c~u + c~v . 8. (c + d)~u = c~u + d~u. 9. c(d~u) = (cd)~u. 10. 1~u = ~u. ...
Word Format
... Our initial definition of a vector turns out to be vague and insufficient for more advanced applications. In advanced physics, mathematical equations and entities including vectors are defined by how they behave when the coordinate system is transformed (changed). Since the transformation properties ...
... Our initial definition of a vector turns out to be vague and insufficient for more advanced applications. In advanced physics, mathematical equations and entities including vectors are defined by how they behave when the coordinate system is transformed (changed). Since the transformation properties ...
