'Singular matrix' presentation slideshows

Matrices

Matrices. Introduction. Matrices - Introduction. Matrix algebra has at least two advantages: Reduces complicated systems of equations to simple expressions Adaptable to systematic method of mathematical treatment and well suited to computers. Definition:

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PROGRAMME 5

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Inverse and Elementary Matrices

Inverse and Elementary Matrices. ??? (inverse matrix). Let. If there is a matrix. such that. then (1) A is called an invertible or nonsingular matrix (2) B is the inverse matrix of A. Note :.

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Warm-Up

Warm-Up. Is matrix multiplication commutative? P 539 # 1,3,5, 11 a b c and d, 19, 20, 32. Accelerated Pre-Calculus Lesson 2 Essential Question: What is an inverse, how can I find the inverse of a matrix, and verify it is the inverse? How can I find the determinant of a square matrix?

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Ordinary least squares regression (OLS)

Ordinary least squares regression (OLS). Minimize Solve the equation system that can be written where is a matrix of observed x -variables. Ridge regression. Minimize

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CS 395/495-26: Spring 2004

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LINEAR MODELS AND MATRIX ALGEBRA - Part 3

LINEAR MODELS AND MATRIX ALGEBRA - Part 3. Chapter 4 Alpha Chiang, Fundamental Methods of Mathematical Economics 3 rd edition. Identity Matrix. Characteristics: It is like the number 1: a(1) = (1)a=a. IA = AI = A. Identity Matrix.

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If a square matrix A has NO inverse then it is called a singular matrix .

Given a n x n matrix A, if there exists an inverse (A -1 ) of matrix A then A A -1 = A -1 A = I n. If a square matrix A has NO inverse then it is called a singular matrix. If a square matrix has an inverse it is called a nonsingular matrix.

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