Characteristic Roots and Characteristic Vectors - Example 1.3 скачать в хорошем качестве

Characteristic Roots and Characteristic Vectors - Example 1.3

In this lecture we continue looking at examples of the use of characteristic roots and characteristic vectors to calculate functions and determine properties of the square, symmetric matrix from which they were obtained. In this lecture we work through Example 1.3. Next lecture in this series:    • Statistical Inference Procedures   Previous lecture in this series:    • Characteristic Roots and Characteristic Ve...   First lecture in this series:    • Introduction to Linear Regression   Here is the textbook we are using: Title: "Introduction to Linear Regression Analysis 5th Edition" Authors: Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining. ISBN-13: 978-0470542811 ISBN-10: 0470542810 Link on Amazon: https://www.amazon.com/Introduction-R... Software Packages Used: Get access to SAS for free: https://www.sas.com/en_us/software/on... Minitab: https://www.minitab.com/en-us/ Chapters 0:00 Introduction 0:25 Description of the 2x2 Matrix and Questions to be Answered 3:20 Calculating the Characteristics Roots of the Matrix 5:35 Finding Characteristic Vectors of the Matrix 19:45 Verify that Characteristic Vectors Corresponding to Different Characteristic Roots Are Orthogonal 20:48 Verify that the Sum of the Characteristic Roots is Equal to the Trace of the Matrix 21:42 Verify that the Product of the Characteristic Roots is Equal to the Determinant of the Matrix 22:50 Is the Matrix a Valid Covariance Matrix? 24:08 Could the matrix be the covariance matrix of a multivariate Normal distribution? If so, which one, and would that distribution possess a pdf?