lecture7_web - L7-1 EEL 6550 Noise in Linear Systems...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
L7-1 EEL 6550 Noise in Linear Systems Lecture 7 I NTRODUCTION TO A BSTRACT A LGEBRA DEFN A binary operation * on a set G is a rule that for each a G, b G assigns c = a * b , such that c G . DEFN A group consists of a set G and a binary operation * with the following properties: 1. Associativity ( a * b ) * c = a * ( b * c ) for a, b, c G 2. Existence of Identity There exists e G such that a * e = e * a = a , for all a G 3. Existence of Unique Inverses For each a G , there exists a unique element a - 1 G such that a * a - 1 = a - 1 * a = e DEFN A group is said to be commutative or abelian if it also satisfies: 4. Commutativity : For all a, b G , a * b = b * a If a group is commutative, then the group operation is often represented as “ + Examples of groups: The set of integers forms a commutative group under addition . The set of integers does not form a group under multiplication . Why? The set of rational numbers excluding zero forms a group under multiplication .
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the 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