Vector spaces vector let 0 denote the zero vector a

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ; are called basis vectors, and Ax, Ay and Az are the x, basis and y and z–components (scalars). The basis components vectors represent fundamental directions in 3– dimensional space, and any vector can be dimensional written in the above form. Vector Spaces Vector Let 0 denote the zero vector. A vector space Let vector is the set of vectors together with an addition and a scalar multiplication subject to the following axioms: following (A + B) + C = A+ (B + C) C) c (A + B ) = c A + c B ( c + d ) A = cA + d A (cd)A = c(dA) A+0=A (1)A = A A + (– A ) = 0 Scalar Multiplication Scalar Given a vector a, we can Given we produce a “new” vector by using scalar multiplication. If we multiply by –1 then the direction of the “new” vector is opposite to the direction of a. If we multiply by 2 then If the length of the “new” vector is twice as long as the vector a. Two Interpretations of Vector Addition Addition Parallelogram Rule: Triangle Rule: Triangle...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern