# Matrix Algebra (Summer I 2014)

## Instructor Information

• Instructor: Will Gunther
• Email: wgunther@andrew.cmu.edu
• Office: Wean 6211
• Office Hours:
• Monday 4:00 - 5:00
• Tuesday 2:00 - 3:00
• Wednesday 4:00 - 5:00
• Thursday 2:00 - 3:00
• Friday 4:00 - 5:00

## Course Information

• Course Title: Matrix Algebra
• Course Number: 21-241
• Lecture Room: Hamerschlag Hall B131
• Lecture Time:
• Monday 10:30 - 11:50
• Tuesday 10:30 - 11:50
• Wednesday 10:30 - 11:50
• Thursday 10:30 - 11:50
• Friday 10:30 - 11:50
• Syllabus: PDF
• Text: Linear Algebra: A Modern Introduction, 3rd Edition by David Poole

## Course Summary

This is an introductory course in matrix algebra (also called linear algebra). Matrix algebra is an extremely important area of both pure and applied mathematics. The basic ideas present themselves in any higher lever math course, and they also appear in other fields such as physics, engineering, industry, finance, and computer science.

The basic idea of matrix algebra is to explore a particular class of functions with (linear transformations) over a particular kind of object (vector spaces). We'll talk about the motivation for this exploration, but this describes a lot of processes that might be of interest. For example, one class of objects we'll talk about is points of space, and the functions that we're interested in on this space correspond to different geometric contortions of the space.

There are no offical prerequisites for this course. As will all math courses at CMU, a fluency with pre-calculus is required. A familiarity with calculus (21-120 and 21-122) is also helpful for some examples we'll see. Concepts of Mathematics (21-127) would be a very helpful course to take before this course as this course will require the writing of formal proofs. But, the course will be (to the best of my efforts) self contained.

There are two goals in this course. The first is to explore theorems and ideas related to linear algebra that will directly help you tackle more difficult course material. The second is to learn and practice your ability to make formal and convincing arguments going indepth into one particular area.

## Course Calendar

May
Monday Tuesday Wednesday Thursday Friday
19
Systems of Linear Equations (2.1)
Notes:
20
Systems represented by matricies (2.2)
Notes:
21
Vectors as Objects (1.1)
Notes:
22
Spanning Sets and Linear Independence (2.3)
Notes:
23
Matricies as Objects (3.1-3.2, 3.6)
Notes:
HW 1:
26
Memorial Day
27
More on Matrix Algebra (3.1-3.2, 3.6)
Notes:
28
Elementary Matricies and Inverse Matrices (3.3)
Notes:
HW 2:
29
Elementary Matricies and Inverse Matrices (3.3)
Notes:
30
Subspaces, Range, Null space (3.5)
Notes:
HW 3:
June
Monday Tuesday Wednesday Thursday Friday
2
Tech Q's: PDF
Exam 1
3
More on Inverses and Subspaces (3.3,3.5)
Notes:
4
Eigenvalues (4.1)
Notes:
5
Determinants (4.2)
Notes:
6
More on Determinants and Eigenvalues (4.1-4.3)
HW 4:
Notes:
9
Similarity and Diagonalization (4.4)
Notes:
10
More on Diagonalization (4.4)
HW 5:
Notes:
11
Applications (3.7, 4.6)
Notes:
12
Inner Products / Orthogonality (5.1)
Notes:
13
Orthogonal Completements and Orthogonal Projections (5.2)
Notes:
HW 6:
16
Tech Q's: PDF
Exam 2
17
More on othogonality (5.2,5.3)
Notes:
18
Gram Schmidt (5.3)
Notes:
19
Abstract Vector Spaces (6.1)
Notes:
20
Abstract Linear Indepndence, Basis, and Dimension (6.2)
HW 7:
Notes:
23
Change of Basis (6.3)
Notes:
24
Linear Transformations; Kernel and Range (6.4-6.5)
Notes:
25
The Matrix of a Linear Transformation (6.6)
Notes:
26
HW 8: Prob
27
Tech Q's: PDF
Exam 3