2016　Linear Algebra II

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Basic science and technology courses
Instructor(s)
Mizumoto Shin-Ichiro
Class Format
Lecture
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(H101)  Fri1-2(H101)
Group
M(1〜10)
Course number
LAS.M106
Credits
2
2016
Offered quarter
3Q
Syllabus updated
2017/1/11
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

Building on the content of "Linear Algebra I", the instructor will explain the fundamentals of vector spaces and linear mapping, eigenvalues and diagonalization, and the inner product of vector spaces.

The aim of this course is to explain the theory of vector spaces which will be important for science and engineering.

Student learning outcomes

This course follows "Linear Algebra I: Exercise". Students will acquire the fundamentals of linear algebra. They will also deepen and further develop their understanding of content learned in "Linear Algebra I".

Keywords

Vector space, basis, linear transformation, eigenvalue, diagonalization

Competencies that will be developed

 Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

Class flow

Aside from the lecture, exercises will be done once a week in tune with the progress of the lecture.

Course schedule/Required learning

Course schedule Required learning
Class 1 Vector space, subspace Understand basics of vector spaces.
Class 2 Linear combination, linear independence, linear dependence 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.

Textbook(s)

M. Saito: Introduction to Linear Algebra (Japanese), Publisher: Tokyo daigaku shuppan kai.

Reference books, course materials, etc.

None in particular

Assessment criteria and methods

Based on overall evaluation of the results for quizzes, report, mid-term and final examinations. Details will be announced in class.

Related courses

• LAS.M102 ： Linear Algebra I / Recitation
• LAS.M108 ： Linear Algebra Recitation II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students are supposed to have completed Linear Algebra I / Recitation (LAS.M102).
Students must register Linear Algebra Recitation II (LAS.M108).

Other

None in particular.