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.
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".
Vector space, basis, linear transformation, eigenvalue, diagonalization
|Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
Aside from the lecture, exercises will be done once a week in tune with the progress of the lecture.
|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||Basis, dimension||Understand basis and dimension of vector spaces.|
|Class 4||Existence of basis||Understand a proof of the existence of a basis.|
|Class 5||Linear transformation, kernel and image||Understand linear transformation and related notions.|
|Class 6||Representation matrix of linear transformation||Understand the representation matrix of linear transformation.|
|Class 7||Inner product and norm, Schwarz's inequality||Understand the definition and properties of inner product and norm.|
|Class 8||Orthonormal basis, orthogonalization method of Schmitt||Understand orthogonality and related notions.|
|Class 9||Coordinate transformation, orthogonal matrix, unitary matrix||Understand coordinate transformation and related notions.|
|Class 10||Eigenvalue, eigenvector||Understand the definition of an eigenvalue and an eigenvector.|
|Class 11||Characteristic polynomial, multiplicity, eigenspace||Understand the properties of eigenvalues.|
|Class 12||Triangularization of matrices||Understand the triangularization of matrices.|
|Class 13||Diagonalization of matrices||Understand diagonalization of matrices.|
|Class 14||Diagonalization of normal matrices, diagonalization real symmetric matrix||Understand notions related to diagonalization.|
|Class 15||Advanced topics||Understand advanced topics on Linear Algebra.|
Saito, Masahiko, Introduction to Linear Algebra, University of Tokyo Press, ISBN978-4130620017
None in particular
Based on overall evaluation on the results of quizzes, reports, mid-term and final examinations. Details will be announced in class.
Students are supposed to have completed Linear Algebra I / Recitation (LAS.M102).
Students must register Linear Algebra Recitation II (LAS.M108).
None in particular.