MAT 213: LINEAR ALGEBRA II
COURSE OUTLINE
TOPIC ONE: INNER PRODUCT SPACE
 Definitions of inner product, Inner product space, the norm
 Cauchy-Schwarz inequality
 Orthogonality,
 Orthonormal sets
 Gram-Schmidt orthogonalization process
TOPIC TWO: LINEAR TRANSFORMATIONS AND MATRICES
 Matrix representation of a linear operator relative to the standard basis.
 Matrix representation of a linear operator relative to an arbitrary basis.
 Coordinate vector and their use.
 Change of basis matrices and their use.
 Similar matrices and diagonalization; diagonalizable operators
TOPIC THREE: EIGENVALUES AND EIGENVECTORS
 Polynomial of matrices and linear operators.
 Characteristic polynomial of a matrix.
 The Cayley Hamilton theorem
 Eigenvalues and eigenvectors computation.
 Eigenvalues, eigenvectors and Diagonalization.
 Orthogonal diagonalization.
TOPIC FOUR: QUADRATIC FORMS
 Definitions.
 Deriving a quadratic form in two, three variables.
 Obtaining a quadratic form of simple 2 x 2, 3 x 3 symmetric matrices.
Page 1 of 3
GRADING
Your grade will be based on 2 sit in C. A. T’s and a final exam with suggested dates below. Content
coverage of CATS is estimated as per the table. Sample CAT and exam will be forwarded in the common
email. The CATS and Exam will be weighed as follows:
C. A. T’s
30 marks
Final Exam
70 marks
Total
100 marks.
The grading scale is A: 70 and above; B: 60 – 70; C: 50 – 60; D: 40 – 50 E: Below 40.
Common email is:
Course Coordinator: Mr. P. Kimani
DATES
DATE
CAT 1
CAT 2
WK
6
11
EXAM
14/15
COVERAGE


Topic 1 - 3
All other remaining part of the
course.
All portions of course
RESULTS DEADLINE
WK
DATE
6
11
6 wks
later
MAT 213 LINEAR ALGEBRA 2
DETAILED COURSE OUTLINE 2021/2022
MON
TH
OCTOBER
WK
No. DATES
0
4th – 8th
11th –
1
15th
2
18th –
22nd
OCTOBER
3
25th –
29th
NOVEMBER
4
NOVEMBER
5
1ST –
5TH
8TH –
12TH
15TH –
19TH
6
TOPIC
SUB TOPIC
Reporting and Registration
Definition, familiar vectors, denotation
Addition, scalar multiplication of vectors
Dot and cross product
Orthogonal vectors
Orthogonal projections.
TOPIC 1 : INNER PRODUCT SPACES
Definitions of inner product, Inner product
space.
The norm; Cauchy-Schwarz inequality
Orthogonality. Orthogonal and
orthonormal sets
Gram-Schmidt orthogonalization process
VECTORS
C.A.T ONE
CAT ONE AND ITS REVISION
Covers all of the above areas
TOPIC 2: LINEAR TRANSFORMATIONS
NOVEMBER
7
22ND –
26TH
Matrix representation of a linear operator
relative to the standard basis.
Matrix representation of a linear operator
relative to an arbitrary basis.
Page 2 of 3
REM
ARKS
MONTH
NOVEMBER
WK
No. DATES
8
29TH
Nov –
3rd Dec
TOPIC
SUB TOPIC
Coordinate vector and their use.
Change of basis matrices and their use.
Similar matrices and diagonalization,
diagonalizable operators
REM
ARKS
TOPIC 3: EIGENVALUES AND EIGENVECTORS
9
6TH –
10TH
10
13TH –
17TH
Q
Polynomial of matrices and linear
operators; evaluating a polynomial using
matrices. Characteristic polynomial of a
matrix.
The Cayley Hamilton theorem
Eigenvalues and eigenvectors
computation.
Eigenvalues, eigenvectors and
Diagonalization.
Orthogonal diagonalization.
DECEMBER
TOPIC 4: QUADRATIC FORMS
11
20TH –
24TH
JANUARY
2022
12
3RD –
7TH
JANUARY
2022
13
Definitions; Deriving a quadratic form in
two, three variables.
Obtaining a quadratic form of simple 2 x
2, 3 x 3 symmetric matrices.
C.A.T TWO
CAT TWO AND ITS REVISION
Covers everything done after the
first CAT.
STUDENTS REVISION AND EXAMS
14
Class Representative Name: ___________________ Sign: _______________ Date: ______________
Course Lecturer: Mr. P. Kimani
Sign: ______________________
Page 3 of 3
Date: _______________