2016 Linear Algebra Recitation II

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Academic unit or major
Basic science and technology courses
Minagawa Tatsuhiro 
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Course description and aims

Based on "Linear Algebra I", this course discusses basic part of vector space and linear mapping, eigenvalue and diagonalization, and inner product of vector space.

The aim of this recitation is to cultivate a better understanding of the theory of vector spaces which will be important for
science and engineering.

Student learning outcomes

Following "Linear algebra I", this course is concerned with the foundation of linear algebra. This course aims for a deeper understanding and development of the theory of Linear Algebra.


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

A recitation class is held every week in accordance with the progress of the lectures.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Vector space, subspace Help better understand the notions of vector space.
Class 2 Linear combination, linear independence, linear dependence,inner product and norm, Schwarz's inequality Help better understand the notion of linear independence.
Class 3 Basis, dimension, existence of basis Help better understand the notion of basis.
Class 4 Orthonormal basis, orthogonalization method of Schmitt,coordinate transformation, orthogonal matrix, unitary matrix Help better understand orthonormal basis and related notion.
Class 5 Linear transformation, kernel and image, basis, dimension, representation matrix of linear transformation Help better understand linear transformation and related notions.
Class 6 Eigenvalue, eigenvector, characteristic polynomial, multiplicity, eigenspace Help better understand eigenvalue problems.
Class 7 Triangularization of matrices, diagonalization of matrices Help better understand diagonalization and related notions.
Class 8 Diagonalization of normal matrices, real symmetric matrix, advanced topics Help better understand real symmetric matrices and related notions.


Takeshi Kajiwara, Introduction to linear spaces, Nihon Hyoronsha

Reference books, course materials, etc.

Takeshi Kajiwara, Lectures on linear algebra, Nihon Hyoronsha
Takeshi Kajiwara, The secret to linear algebra, Kyoritsu shuppan

Assessment criteria and methods

Based on overall evaluation of the results for quizzes, report, mid-term and final examinations.

Related courses

  • LAS.M102 : Linear Algebra I / Recitation
  • LAS.M106 : Linear Algebra II

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

Students are supposed to have completed Linear Algebra I / Recitation (LAS.M102).
Students are required to register Linear Algebra II (LAS.M106).


None in particular.

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