90 件ヒット (0.024秒)：
線形代数学AおよびBでは、行列の基本的な演算や行列式から概ね行列の対角化まで、主として数ベクトルのなす空間の基底や次元などの基本的事項とともに学んだ。この代数学序論Bでは、これらに引き続いて、一般のベクトル空間と線型写像について学ぶ。
特に、ジョルダン標準形と呼ばれる、対角化が必ずしもできない場合の標準形が一つの目標となるが、そのためにもベクトル空間の直和、商空間、テンソル積といわれるベクトル空間の間に定義される演算や、群・環・体という代数学における基本概念についても、体系的に述べるための言葉として慣れることがもう1つの目標となる。
In linear algebra A and B, we treat basics in matrix algebras such as determinants or diagonalization, together with basic notion for vector spaces such as basis or dimension. Following these knowledge we will treat general vector spaces as well as linear maps.
In particular we will learn so called Jordan canonical form for a linear transform in case of diagonalization is not possible, which will be one of the goal of the course. To describe things systematically we will need operations for vector spaces, namely direct sums, quotients and tensor products, together with basic notion in algebra such as groups, rings and fields. To become familiar with these will be another goal of the course.
線形代数学Aに引き続き、ベクトル空間の基底、次元、固有値、内積、行列の標準化などを扱い、
基礎的な計算力を身につけつつ線形代数学の初歩を学ぶ。
This course is a continuation of Linear Algebra, A. It covers the general notion of vector spaces and related notions such as basis, dimension, inner products, eigenvalues, and normal forms of matrices. Students will learn computational techniques along the way.
線形代数学Aに引き続き、ベクトル空間の基底、次元、固有値、内積、行列の標準化などを扱い、
基礎的な計算力を身につけつつ線形代数学の初歩を学ぶ。
This course is a continuation of Linear Algebra, A. It covers the general notion of vector spaces and related notions such as basis, dimension, inner products, eigenvalues, and normal forms of matrices. Students will learn computational techniques along the way.
線形代数学Aに引き続き、ベクトル空間の基底、次元、固有値、内積、行列の標準化などを扱い、
基礎的な計算力を身につけつつ線形代数学の初歩を学ぶ。
This course is a continuation of Linear Algebra, A. It covers the general notion of vector spaces and related notions such as basis, dimension, inner products, eigenvalues, and normal forms of matrices. Students will learn computational techniques along the way.
行列の固有値と固有ベクトル，対角化，三角化を学ぶ．また，内積が定義されているベクトル空間について基本概念を学ぶ．さらに，線形代数の応用例を学ぶ．
Eigenvalues and eigenvectors of matrices are introduced. Using these concepts, students will learn diagonalization and triangularization of matrices. Furthermore, vector spaces with inner product will be treated. Finally, applications of linear algebra to various specialized topics
will be mentioned.
行列の固有値と固有ベクトル，対角化，三角化を学ぶ．また，内積が定義されているベクトル空間について基本概念を学ぶ．さらに，線形代数の応用例を学ぶ．
Eigenvalues and eigenvectors of matrices are introduced. Using these concepts, students will learn diagonalization and triangularization of matrices. Furthermore, vector spaces with inner product will be treated. Finally, applications of linear algebra to various specialized topics
will be mentioned.
行列の固有値と固有ベクトル，対角化，三角化を学ぶ．また，内積が定義されているベクトル空間について基本概念を学ぶ．さらに，線形代数の応用例を学ぶ．
Eigenvalues and eigenvectors of matrices are introduced. Using these concepts, students will learn diagonalization and triangularization of matrices. Furthermore, vector spaces with inner product will be treated. Finally, applications of linear algebra to various specialized topics will be mentioned.
行列の固有値と固有ベクトル，対角化，三角化を学ぶ．また，内積が定義されているベクトル空間について基本概念を学ぶ．さらに，線形代数の応用例を学ぶ．
Eigenvalues and eigenvectors of matrices are introduced. Using these concepts, students will learn diagonalization and triangularization of matrices. Furthermore, vector spaces with inner product will be treated. Finally, applications of linear algebra to various specialized topics
will be mentioned.
行列の固有値と固有ベクトル，対角化，三角化を学ぶ．また，内積が定義されているベクトル空間について基本概念を学ぶ．さらに，線形代数の応用例を学ぶ．
Eigenvalues and eigenvectors of matrices are introduced. Using these concepts, students will learn diagonalization and triangularization of matrices. Furthermore, vector spaces with inner product will be treated. Finally, applications of linear algebra to various specialized topics
will be mentioned.
行列の固有値と固有ベクトル，対角化，三角化を学ぶ．また，内積が定義されているベクトル空間について基本概念を学ぶ．さらに，線形代数の応用例を学ぶ．
Eigenvalues and eigenvectors of matrices are introduced. Using these concepts, students will learn diagonalization and triangularization of matrices. Furthermore, vector spaces with inner product will be treated. Finally, applications of linear algebra to various specialized topics
will be mentioned.