今日的科學已逐漸數量化，常常需要對從實驗室或調查得來的大量數據或測度作分析。在統計及數量方法的運算中，矩陣代數可明白地、簡潔地表示龐大的數量資料。收集、整理及表達資料常借助矩陣代數作為工具，故矩陣代數已成為現今在科學研究及實務運算上不可或缺的數學工具。因此，本課程的目的即在學習矩陣代數的理論基礎及在統計上的應用。
The purpose of this course is to familiarize the students with the basic concepts and results of matrix algebra. It's designed to provide the tools needed for the understanding of a wide variety of topics in statistics, where the matrices are used, such as linear models and multivariate analysis, among others.
We shall introduce the theoretical development in the course with numerous examples to motivate the learning of the theory. It is essential that students obtain a firm understanding of the effectiveness of using such theory in statistics.Today's science has become increasingly quantitative, often requiring the analysis of large amounts of data or measurements obtained from laboratories or surveys. In the operation of statistical and quantitative methods, matrix algebra can represent huge quantitative data clearly and concisely. Matrix algebra is often used as a tool to collect, organize and express data. Therefore, matrix algebra has become an indispensable mathematical tool in today's scientific research and practical operations. Therefore, the purpose of this course is to learn the theoretical basis of matrix algebra and its applications in statistics.
The purpose of this course is to familiarize the students with the basic concepts and results of matrix algebra. It's designed to provide the tools needed for the understanding of a wide variety of topics in statistics, where the matrices are used, such as linear models and multivariate analysis, among others.
We shall introduce the theoretical development in the course with numerous examples to motivate the learning of the theory. It is essential that students obtain a firm understanding of the effectiveness of using such theory in statistics.
今日的科學已逐漸數量化，常常需要對從實驗室或調查得來的大量數據或測度作分析。在統計及數量方法的運算中，矩陣代數可明白地、簡潔地表示龐大的數量資料。收集、整理及表達資料常借助矩陣代數作為工具，故矩陣代數已成為現今在科學研究及實務運算上不可或缺的數學工具。因此，本課程的目的即在學習矩陣代數的理論基礎及在統計上的應用。
修習本課程所需具備的數學基礎訓練，只要求具有高中程度的代數及簡單的微分訓練即可。課程內容包含：矩陣的基本運算及性質、行列式、特殊矩陣的介紹、反矩陣、秩、廣義逆(反)矩陣、分割矩陣、線性方程式、特徵值及特徵向量、及統計上的應用。
Today's science has become increasingly quantitative, often requiring the analysis of large amounts of data or measurements obtained from laboratories or surveys. In the operation of statistical and quantitative methods, matrix algebra can represent huge quantitative data clearly and concisely. Matrix algebra is often used as a tool to collect, organize and express data. Therefore, matrix algebra has become an indispensable mathematical tool in today's scientific research and practical operations. Therefore, the purpose of this course is to learn the theoretical basis of matrix algebra and its applications in statistics.
The basic mathematics training required to study this course only requires high school level algebra and simple differential calculus training. Course content includes: basic operations and properties of matrices, determinants, introduction to special matrices, inverse matrices, ranks, generalized inverse (inverse) matrices, partitioning matrices, linear equations, eigenvalues and eigenvectors, and statistical applications.
Matrix Algebra Useful for Statistics, by Shayle R. Searle
matrix algebra useful for statistics, by SHA with R. Searle
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| Midterm ExamMidterm Exam midterm exam |
40 | |
| Final ExamFinal Exam final exam |
40 | |
| AttendanceAttendance attendance |
20 |
