Matrix Theory | MSc in Electronics and Technology

Course overview

The aim of this course is to learn and master the basic theory and method of Matrix theory. The course covers linear space and linear transformation, Euclidean space and unitary space, as well as the linear transformation on this space, and profoundly reveals the essence and thought of linear transformation on finite dimensional space.

What you will learn

Summarize the concepts related to linear space, master the linear transformation and its matrix representation, and master the concepts related to Euclidean space.

Master the concept of vector norm and matrix norm and their calculation.
Master the concept of matrix series and matrix series, be able to find the limit of matrix series and determine the convergence of matrix power series; master the representation of matrix function and its corresponding calculation method.
Master the triangular decomposition, QR decomposition, full rank decomposition and singular value decomposition of matrices.
Formulate the estimation of eigenvalue bounds, master Gerschgorin’s disc theorem and its extensions, and understand the generalized eigenvalue problem.
Master the concept and computation of generalized inverse matrices and be able to use this concept for theoretical analysis of solutions of systems of linear equations.

Meet your instructor

Tieming Xiang

Course content

Session 1: Linear space and linear transformation （part 1）
Session 2: Linear space and linear transformation （part 2）
Session 3: vector norm and the matrix norm
Session 4: the common norm compatibility
Session 5: Matrix analysis （part 1）
Session 6: Matrix analysis（part 2）
Session 7: The linear constant function differential equation
Session 8: Four matrix decomposition method
Session 9: The characteristic value estimation and Gail round
Session 10: The linear constant function differential equation
Session 11: Matrix decomposition
Session 12: Eigenvalue estimation
Session 13: Generalized inverse matrix

Teaching methodology

Lectures, group discussion and problem solving

Assessment

Midterm exam (40%) Will include combination of numerical exercises and open-ended theoretical questions.
Final written exam (60%) Will include combination of numerical exercises and open-ended