forecasting_lecture_02

forecasting_lecture_02 - 1 Lecture Notes 2 1 Review of...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Lecture Notes 2 1. Review of Matrices The ability to manipulate matrices is critical in economics. 1. Matrix – a rectangular array of numbers, parameters, or variables placed in rows and columns. Matrices are associated with linear equations. Elements ij a denotes the element in row i and column j. column vector – one column of elements row vector – one row of elements Examples 5 1 7 1 8 3 7 6 7 4 3 5 5 2 3 4 3 2 1 8 6 2 3 6 5 4 7 8 9 D C B A (a) What is the dimension of each matrix? Write as G m,n . (b) Which matrix is a square matrix? Column vector? Row vector? (c) What is the value for the following elements a 2,3 , b 1,1 , c 2,1 , and d 3,3 ? 2. Multiplication by a scalar – multiplying every element of a matrix by the scalar Scalar is a number If w = 3, then wA = ? 2 3. Two matrices can be added or subtracted only if they have the same dimensions. The commutative law of addition hold for matrices, H + K = K + H 4 10 4 1 21 2 6 5 4 7 8 9 E A Find A – 2E? 4. matrix multiplication – requires a conformability condition. 3 5 7 8 6 2 4 1 R and H We want to multiply S = H R Check the dimensions for H 3,2 and R 2,1 . The number of columns in H equals the number of rows in R Therefore, the matrices are conformable for multiplication. The dimension of S 3,1 . 61 28 17 3 7 5 8 3 6 5 2 3 4 5 1 3 5 7 8 6 2 4 1 R H S Note – The commutative law of multiplication never holds for matrix multiplication, A B B A The distributive law holds for matrix multiplication, A(B+C)=AB+AC or (B+C)A=BA+BC? 5. An identity matrix (usually denoted by I) is a square matrix with ones in its principle diagonal (the diagonal running northwest to southeast) and zeros everywhere else. 3 Write identity matrices of dimensions: 3 x 3, 5 x 5, and 3 x 6. Any matrix multiplied by the identity matrix gets that same matrix again 7 8 6 2 4 1 1 7 8 1 6 2 1 4 1 7 1 8 6 1 2 4 1 1 1 1 7 8 6 2 4 1 I H 6. Transpose – interchange the rows and columns of a matrix....
View Full Document

This note was uploaded on 04/05/2012 for the course ECON 421 taught by Professor Blair during the Fall '11 term at Rutgers.

Page1 / 15

forecasting_lecture_02 - 1 Lecture Notes 2 1 Review of...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online