2019 Linear Algebra Recitation II N(11~20)

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Academic unit or major
Basic science and technology courses
Kawai Shingo 
Class Format
Media-enhanced courses
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Academic year
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Syllabus updated
Lecture notes updated
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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. Details will be announced in class.

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 Help better understand the notion of linear independence.
Class 3 Basis, dimension, existence of basis Help better understand the notion of basis.
Class 4 Linear transformation, kernel and image, representation matrix of linear transformation Help better understand linear transformation and related notions.
Class 5 Orthonormal basis, inner product and norm, Schwarz's inequality, orthogonalization method of Schmitt Help better understand orthonormal basis and related notion.
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, diagonalization of real symmetric matrix Help better understand diagonalization of matrices and related notions.


See the syllabus of "Linear Algebra II N".

Reference books, course materials, etc.

None in particular.

Assessment criteria and methods

Based on overall evaluation on the results of quizzes, reports, 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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