This preview shows pages 1–2. Sign up to view the full content.
Discussion Section Notes  Matrices
Everything You Need to Know About Matrices
Conceptually
matrices are an extension of onedimensional math
1dimensional
ndimensional
values
scalar
vector
mapping effect(s)
of multiplication
stretch/compress, flip
stretch/compress, flip
multiplication
condition to
reduce dimension
0 (to a single point)
determinant=0
(singular matrix,
maps to a line or
single point)
multiplication
commutes
yes
no
multiplicative
inverse
yes (if x <> 0)
yes (if det <> 0)
Types of Matrices, Matrix Properties
•
diagonal
•
index
•
determinant
•
trace
•
positive, nonnegative
•
primitive
Determinants
real number, not a matrix (can be < 0)
can only take the determinant of a square matrix
if det = 0
the matrix doesn’t have an multiplicative inverse
determinant of a 2x2 matrix: ad – bc
taking the determinant of a 3 x 3 matrix (see
http://www.richland.cc.il.us/james/lecture/m116/matrices/determinant.html
)
Finding the Inverse
question: can a nonsquare matrix have an inverse?
minor for a specific element in a matrix: the determinant of the matrix that results when you
eliminate the row and column of that element
cofactor of the element in row r column j: (–1)
r+j
x the minor for that element. In other words
cofactor is determinant of the matrix that results when you eliminate row r and column j,
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '10
 WayneM.Getz

Click to edit the document details