MTH 204

MTH 204, Liner Algebra II, for Mathematics students (Session 2015-2016)

Instructor: Haridas Kumar Das, Office: Room No.: 318, Annex Building (Kaji Motahar Hossain), Phone: 01672711080, Email: hkdas_math@du.ac.bd

Office Hours:

Office Hours for Theory Course:

Sunday : 1:00 PM - 2 : 00 PM

Tuesday : 11:00 AM - 12 : 00 PM

Wednesday : 2:00 PM - 3 : 00 PM

/ or by appointment.

Important dates:

First (1st) Incourse Date: 25/05/2017(Thursday), Time : 2.00 PM-3.00 PM.

Short Quiz Date: 16/07/2017(Sunday), Time : 1.30 PM-2.00 PM. Syllabus: Inner products. Inner product spaces, Orthogonality and orthonormal sets.

Second (2nd) Incourse Date: 25/09/2017(Monday), Time : 2.00 PM-3.00 PM.

MTH 204: Linear Algebra II 3 credits

1. Similar Matrices: Canonical forms of matrices, Symmetric, orthogonal and Hermitian matrices

2. Linear Functional and dual Space: Linear transformation and their properties. Matrix representation of linear transformations. Change of bases. Linear functional and the dual space; Dual basis, Second dual space; Annihilators; Transpose of a linear transformation

3. Orthogonality: Inner product, Length and Orthogonality; Projections and Least Squares; The Gram-Schmidt process; Orthonormal sets; Inner product spaces; Linear functions and adjoints; Positive operators; unitary operators and normal operators; The spectral theorem; Application to Linear Models and Fourier Approximation

4. Bilinear, quadratic & hermitian forms: Matrix form; transformations; canonical forms; reduction form; definite and semi-definite forms; principal minors; and factorable forms

5. Symmetric Matrices and Quadratic Forms: Diagonalization of Symmetric Matrices; Quadratic Forms; The Singular Value Decomposition ; Applications to Image Processing and Statistics

6. Positive Definite Matrices: Minima, Maxima, and Saddle Points; Tests for Positive Definiteness; Minimum Principles.

Evaluation: Incourse Assessment 30 Marks. Final examination (Theory, 3 hours) 70 Marks

Eight questions of equal value will be set, of which any five are to be answered.

References:

  1. H. Anton, and C.Rorres, Linear Algebra with Applications, 9thed

  2. David C. Lay, Linear Algebra and Its Applications, 4thed

  3. W. K. Nicholson, Linear Algebra with Applications, 3rded

  4. S. Lipshutz, Linear Algebra, Schaum’s Outline Series.

  5. G. Strang, Linear Algebra and Its Applications, 4thed

  6. B Kolman and D R. HilL, Elementary Linear Algebra with Applications.

Evaluation

Incourse Assessment 30 Marks. Final examination (Theory, 3 hours) 70 Marks. Eight questions of equal value will be set, of which any five are to be answered.

Note: If you have any question regarding CT and attendance Marks please talk to me of course before August 04, 2019, Sunday, (12PM-1:00PM).

Results of assignments and tests are in the following attachments. (please report any errors to hkdas_math@du.ac.bd )

Final update Result of the 2nd year Honors Incourse Assesment Examination, 2019.