Lecture 1 Matrix Terminology and Notation, Lecture notes of Linear Algebra

Download Lecture 1 Matrix Terminology and Notation and more Lecture notes Linear Algebra in PDF only on Docsity! Lecture 1 Matrix Terminology and Notation • matrix dimensions • column and row vectors • special matrices and vectors 1–1 Matrix dimensions a matrix is a rectangular array of numbers between brackets examples: A =   0 1 −2.3 0.1 1.3 4 −0.1 0 4.1 −1 0 1.7   , B = [ 3 −3 12 0 ] dimension (or size) always given as (numbers of) rows × columns • A is a 3× 4 matrix, B is 2× 2 • the matrix A has four columns; B has two rows m× n matrix is called square if m = n, fat if m < n, skinny if m > n Matrix Terminology and Notation 1–2 Matrix equality A = B means: • A and B have the same size • the corresponding entries are equal for example, • [ −2 3.3 ] 6= [ −2 −3.3 ] since the dimensions don’t agree • [ −2 3.3 ] 6= [ −2 3.1 ] since the 2nd components don’t agree Matrix Terminology and Notation 1–5 Zero and identity matrices 0m×n denotes the m× n zero matrix, with all entries zero In denotes the n× n identity matrix, with Iij = { 1 i = j 0 i 6= j 02×3 = [ 0 0 0 0 0 0 ] , I2 = [ 1 0 0 1 ] 0n×1 called zero vector ; 01×n called zero row vector convention: usually the subscripts are dropped, so you have to figure out the size of 0 or I from context Matrix Terminology and Notation 1–6 Unit vectors ei denotes the ith unit vector: its ith component is one, all others zero the three unit 3-vectors are: e1 =   1 0 0   , e2 =   0 1 0   , e3 =   0 0 1   as usual, you have to figure the size out from context unit vectors are the columns of the identity matrix I some authors use 1 (or e) to denote a vector with all entries one, sometimes called the ones vector the ones vector of dimension 2 is 1 = [ 1 1 ] Matrix Terminology and Notation 1–7