Based on "Linear Algebra I", this course focuses on basic principles of vector space and linear mapping, eigenvalue and diagonalization, inner produce of vector space.
The aim of this course is to understand the theory of vector spaces which is important in learning science and engineering.
Following "Linear algebra I", this course gives the foundation of linear algebra. This course aims for deeper understanding and development of knowledge on the theory of Linear Algebra.
Vector space, basis, linear transformation, eigenvalue, diagonalization
Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Besides lectures, a recitation class is opened every week in accordance with lectures.
Course schedule | Required learning | |
---|---|---|
Class 1 | Vector space, subspace | Understand basics of vector spaces. |
Class 2 | Linear combination, linear independence, linear dependece | Understand linear independence and related notions. |
Class 3 | Inner product and norm, Schwarz's inequality | Understand the definition and properties of inner product and norm. |
Class 4 | Basis, dimension | Understand basis and dimension of vector spaces. |
Class 5 | Existence of basis | Understand a proof of the existence of a basis. |
Class 6 | Orthonormal basis, orthogonalization method of Schmitt | Understand orthogonality and related notions. |
Class 7 | coordinate transformation, orthogonal matrix, unitary matrix | Understand coordinate transformation and related notions. |
Class 8 | Linear transformation, kernel and image | Understand linear transformation and related notions. |
Class 9 | Representation matrix of linear transformation | Understand the representation matrix of linear transformation. |
Class 10 | Eigenvalue, eigenvector | Understand the definition of an eigenvalue and an eigenvector. |
Class 11 | Characteristic polynomial, multiplicity, eigenspace | Understand basics of vector spaces. |
Class 12 | Triangularization of matrices | Understand the triangularization of matrices. |
Class 13 | Diagonalization of matrices | Understand the diagonalization of matrices. |
Class 14 | Diagonalization of normal matrices, real symmetric matrix | Understand notions related to diagonalization. |
Class 15 | Advanced topics | Understand advanced topics of linear algebra. |
Linear Algebra in English, Catherine Oikonomides, Eiji Yanagida
None in particular
Based on overall evaluation of the results for quizzes, report, mid-term and final examinations. Details will be announced during a lecture.
Students are supposed to have completed Linear Algebra I / Recitation (LAS.M102).
Students must register Linear Algebra Recitation II (LAS.M108).
None in particular.