This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MA 265 LECTURE NOTES: WEDNESDAY, FEBRUARY 13 Real Vector Spaces Vectors in nSpace. Recall that R n is the collection of all real nvectors: x = x 1 x 2 . . . x n where the entries x i are real numbers. We call this collection (real) nspace . The elements x R n will be called vectors. (If the x i are complex numbers, then the collection of all complex nvectors is denoted by C n .) Vectors in R 1 . Consider n = 1. Elements x R 1 will be called scalars for reasons to be discussed later in the lecture. Note that we do not use any special font such as x to denote this. We usually draw real numbers on the real number line: x o /  1   1  2 R 1 Recall that positive is to the right and negative is to the left. Vectors in R 2 . Now consider n = 2. The vectors of interest will be in the form x = x y where x and y are real numbers. We can draw this as a in the Cartesian plane by identifying x with the point P = ( x,y ). These will be called the coordinates of x . Conversely, say that we have two points P = ( x,y ) and Q = ( x ,y ). We can consider the line segment between P and Q , denoted by PQ . However, we are more interested in the directed line segment PQ which begins at with tail P and ends at head...
View
Full
Document
This note was uploaded on 03/11/2010 for the course MA 261A 0026100 taught by Professor ... during the Spring '10 term at Purdue University Calumet.
 Spring '10
 ...

Click to edit the document details