{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MATH2107-4-40 - Section 4.4 Coordinate Systems Linear...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 4.4 Coordinate Systems Linear Algebra and its Applications David C. Lay — Winter 2008 – p. 1/8
Background image of page 1

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

View Full Document Right Arrow Icon
Given a basis B = { b 1 ,..., b n } for a vector space V . For each x V there exists a unique set of scalars c 1 ,c 2 ,...,c n such that x = c 1 b 1 + c 2 b 2 + · · · + c n b n The scalars c 1 ,c 2 ,...,c n are called the coordinates of x relative to the basis B . These coordinates can be denoted by [ x ] B = c 1 . . . c n — Winter 2008 – p. 2/8
Background image of page 2
and called the coordinate vector of x relative to B or the B -coorindate vector of x . The mapping V R n x [ x ] B is called the coordinate mapping. — Winter 2008 – p. 3/8
Background image of page 3

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

View Full Document Right Arrow Icon
Graphical Interpretation Suppose e 1 = bracketleftbigg 1 0 bracketrightbigg , e 2 = bracketleftbigg 0 1 bracketrightbigg are the vectors in the basis B for R 2 . — Winter 2008 – p. 4/8
Background image of page 4
Suppose b 1 = e 1 , b 2 = bracketleftbigg 1 2 bracketrightbigg . Let B 1 = { b 1 , b 2 } . — Winter 2008 – p. 5/8
Background image of page 5

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

View Full Document Right Arrow Icon
Example Let b 1 = bracketleftbigg
Background image of page 6
Background image of page 7

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

View Full Document Right Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}