lect 5 p 1
Lecture 4 continued
Projections of the plane onto a line at
angle T with the x-axis:
the matrix is
Rotations of the plane by an angle T :
the matrix is
Examples are
Maths 253 Lecture 5
Todays topic: Change of basis matrices
and their properties
lect 10 p 1
Maths 253 Lecture 10
Theorem 3.4.7
Todays topic: Markov chains, stochastic
matrices, Invariant subspaces.
Colour code: Orange/Red
Lecture Notes: Sec 3.4, 3.5.
Anton & Busby: Ch 5.1, pp 225 235.
Poole:
See the Textbook Guide at
the back of the
lect 3 p 1
Maths 253 Lecture 3
continued
Todays topic: Basis, Dimension, the
Coordinate Mapping
1.4.3
Colour code: Orange/Red
Lecture Notes: Sec 1.4 1.5.
Anton & Busby: Ch 7.11, pp 439- 431.
(1)
Poole:
If the only way equation (1) can be true
is if
a1 = a
lect 4 p 1
Maths 253 Lecture 3 cont
1.5.3
lect 4 p 2
Maths 253 Lecture 4
Todays topic: Linear Transformations
Colour code: Yellow/Orange
2.1.1
Lecture Notes: Sec 2.1 2.2.
Anton & Busby: Ch 6.1, pp 265 277.
Poole:
See the Textbook Guide at
the back of the
lect 9 p 1
so can find the matrices D and P
for which
D =P1AP
for any diagonalisable operator T,
where [T]E = A
Maths 253 Lecture 9
Todays topic: Applications to discrete
time system evolution
Discrete time systems
evolution
Definition 3.4.1
Colour code:
lect 16 p 1
Maths 253 Lecture 16
Todays topic: Quadratic forms
Colour code: Red
Lecture Notes: Sec 6.1, 6.2.
Anton & Busby: Ch 8.4 pp 481-484,
Ch 8.5, pp 498 - 500.
Poole:
See the Textbook Guide at
the back of the Lecture Notes.
Consolidation: Try exercis
lect 8 p 1
Maths 253 Lecture 8
3.2.2
Todays topic: Diagonalisation
Colour code: Orange
Lecture Notes: Sec 3.2 3.3.
Anton & Busby: Ch 8.2, pp 460 465.
Poole:
See the Textbook Guide at
the back of the Lecture Notes.
Consolidation: Anton & Busby: Try exercis