Essay: Alan Mathison Turing
Turing, born in 1912, was descended from an old Irish family who were known for being
great inventors, engineers and scientists. His grandfather on his fathers side was well known in
Newtons and Babbages old college, Trinity Co
Intermolecular Forces
Intermolecular Forces:
- Forces between molecules
- Responsible for the state of matter: solid, liquid, or gas
- affect the melting and boiling points of compounds as well as the
solubility of one substance in another
- weaker than c
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