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Linear Algebra for AI - Period 4
概述
CEA CAPA 合作伙伴机构: Vrije Universiteit Amsterdam
地点: Amsterdam, 荷兰
Primary Subject Area: 数学
Other Subject Area: 计算机科学
指令: 英语
课程代码: XB_0081
记录来源: 合作伙伴机构
课程详细信息: 200级
Recommended Semester Credits: 3
联系时间: 84
描述
The topics that will be treated are listed below. For every topic, the relevant concepts are listed.
Linear systems: linear system (consistent/inconsistent/homogeneous/inhomogeneous), augmented) coefficient matrix, 行等价, pivot position/column, (reduced) echelon form, 基本/自由变量, 生成集合, parametric vector form, linear (in)dependence.
Linear transformations: linear transformation, (co)域, 距离和图像, 标准矩阵, 一对一和映上, 奇点, 行列式, 初等矩阵.
Subspaces and bases: subspace, column and null space, basis, coordinate system, dimension, rank.
Eigenvalues and 特征向量s: eigenvalue, 特征向量, 特征空间, characteristic equation/polynomial, algebraic multiplicity, 相似, diagonalization and diagonalizability.
Orthogonality: dot product, 规范, 距离, 正交性, orthogonal complement, orthogonal set/basis, orthogonal projection, 正规化, 标准正交基, Gramm-Schmidt process, least squares problem/solution, orthogonal diagonalization, singular value/vector, singular value decomposition, Moore-Penrose inverse.
Vrije Universiteit Amsterdam (VU Amsterdam) awards credits based on the ECTS system. 联系 hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.
Linear systems: linear system (consistent/inconsistent/homogeneous/inhomogeneous), augmented) coefficient matrix, 行等价, pivot position/column, (reduced) echelon form, 基本/自由变量, 生成集合, parametric vector form, linear (in)dependence.
Linear transformations: linear transformation, (co)域, 距离和图像, 标准矩阵, 一对一和映上, 奇点, 行列式, 初等矩阵.
Subspaces and bases: subspace, column and null space, basis, coordinate system, dimension, rank.
Eigenvalues and 特征向量s: eigenvalue, 特征向量, 特征空间, characteristic equation/polynomial, algebraic multiplicity, 相似, diagonalization and diagonalizability.
Orthogonality: dot product, 规范, 距离, 正交性, orthogonal complement, orthogonal set/basis, orthogonal projection, 正规化, 标准正交基, Gramm-Schmidt process, least squares problem/solution, orthogonal diagonalization, singular value/vector, singular value decomposition, Moore-Penrose inverse.
Vrije Universiteit Amsterdam (VU Amsterdam) awards credits based on the ECTS system. 联系 hours listed under a course description may vary due to the combination of lecture-based and independent work required for each course therefore, CEA's recommended credits are based on the ECTS credits assigned by VU Amsterdam. 1 ECTS equals 28 contact hours assigned by VU Amsterdam.
