Similar Matrices and Diagonalizable Matrices
S. F. Ellermeyer
July 1, 2002
1
Similar Matrices
Denition 1 If A and B are nxn (square) matrices, then A is said to be
similar to B if there exists an invertible nxn matrix, P , such that A =
P 1 BP .
Example 2
physics
electric field and electric force
If qs>0, then dir E is away from qs.
If qs<0, then dir E is toward qs.
If q0>0, then dir E =dir F .
If q0<0, then dir E is opposite to dir F .
qs
electric
charge
Gausss Law:
scalar
E dA =
E at a point in space
el
MATH 304
Linear Algebra
Lecture 22:
Matrix of a linear transformation.
Linear transformation
Denition. Given vector spaces V1 and V2 , a
mapping L : V1 V2 is linear if
L(x + y) = L(x) + L(y),
L(r x) = rL(x)
for any x, y V1 and r R.
Matrix transformations
CASCADING IF-ELSE
A cascading if-else is a composite of if-else statements where the false path of the outer
statement is a nested if-else statement. The nesting can continue to several levels.
Cascading if-else Syntax
if ( truth value 1 )
path 1
else
if