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Understanding Matrices and Matrix Arithmetic in MATLAB

This guide provides an overview of matrices and their arithmetic operations using MATLAB. It covers the definition and properties of small matrices, including how to define them, access their elements, and determine their sizes. Additionally, it addresses the concept of square matrices, empty matrices, and applying mathematical functions to matrices. Topics such as colon notation, submatrices, matrix addition, subtraction, and multiplication are also discussed. This resource is essential for anyone looking to grasp matrix operations in MATLAB.

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Understanding Matrices and Matrix Arithmetic in MATLAB

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  1. 13.3 Matrices and Matrix Arithmetic A11 A12 …A1n A= A21 A22 …A2n ： ： ： ： ： ： Am1 Am2 …Amn 13.3.1 Definition and Properties of Small Matrices >>A=[1 2 3 4;5 6 7 8 ;9 10 11 12;13 14 15 16]; and >>A=[ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ] P.S. : Matrix rows are separated by a semicolon a mew line, and the elements within a row of a matrix may be separated by commas as well as a blank. The elements of a matrix are enclosed by brackets.

  2. Accessing Matrix Elements : • Ex2: >>V = [ 5 4 3 2 1 ]; >>V(2) ans = 4 >> • Ex1: >>A(1,2),A(2,3) ans = 2 ans = 7 >> • Size of a Matrix : >>size([1 2 3 4 5 ;6 7 8 9 10 ;11 12 13 14 15 ] ) ans= 3 5 >>

  3. Square Matrices : Equal Matrices : • If a matrix has the same numbers of rows as columns(i.e.,m=n),then we say that it is square. >> A = [ 1 2 3; 4 5 6 ]; >>B=A; B= 1 2 3 4 5 6 >> • Defining Matrices with Built-In MATLAB Functions • Empty Matrices : >> eye(3,4) ans = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 >> >> A=[ ];

  4. 13.3.3 Application of Mathematical Functions to Matrices >>x=[ 1 2 3 4 5; 6 7 8 9 10 ] x= 1 2 3 4 5 6 7 8 9 10 >> then the command >>sin(x) ans = 0.8415 0.9093 0.1411 -0.7568 -0.9589 -0.794 0.6570 0.9894 0.4121 -0.5440

  5. 13.3.4 Colon Notation >> -3 : 3 ans= -3 -2 -1 0 1 2 3 >> The default increment is by 1 but that can be changed. For example : >>x = [0.0:0.1:2.0]’ ; >>y = sin(x); >>[x y] The third command takes the x and y column vectors and places then in a 21-by-2 matrix table.

  6. 13.3.5 Submatrices >> A=[1:6;2:7;4:9]; generates a 3-by-3 matrix >>A(1:4,3) is the column vector consisting of the first four entries of the third column of A >>A(:,3) is the third column of A, and A(1:4;) is the first four rows of A. 13.3.6 Matrix Arithmetic

  7. Matrix Transpose

  8. Matrix Addition and Subtraction

  9. Dot Product Ex : • Matrix Multiplication

  10. Scalar Multiplication of Matrices

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