How To Upload A Matrix Into Matlab

INTRODUCTION TO MATLAB | Matlab Tutorial – You can find all the Matlab tutorial hither. In this tutorial we will discuss about Matrix in MATLAB.

Introduction

Matrices are the basic elements of the MATLAB environment. A matrix is a two-dimensional array consisting of m rows and n columns. Special cases are column vectors (n = ane) and row vectors (grand = ane).

In this department we volition illustrate how to apply dissimilar operations on matrices. The following topics are discussed: vectors and matrices in MATLAB, the changed of a matrix, determinants, and matrix manipulation.

MATLAB supports two types of operations, known as matrix operations and array operations. Matrix operations will be discussed first.

Matrix generation

Matrices are fundamental to MATLAB. Therefore, we need to become familiar with matrix generation and manipulation. Matrices tin be generated in several ways

Entering a vector

A vector is a special case of a matrix. The purpose of this section is to show how to create vectors and matrices in MATLAB. As discussed earlier, an array of dimension 1 ×due north is called a row vector, whereas an array of dimension m × 1 is called a cavalcade vector. The elements of vectors in MATLAB are enclosed by square brackets and are separated by spaces or by commas. For example, to enter a row vector, v, type

>> v = [1 4 7 10 xiii]

five = 1 4 7 ten 13

Column vectors are created in a like style, however, semicolon (;) must divide the components of a column vector,

>> w = [i;4;7;x;13]

due west = 1

4

7

10

13

On the other paw, a row vector is converted to a column vector using the transpose operator. The transpose operation is denoted by an apostrophe or a unmarried quote (').

>> w = 5'

w = 1

4

vii

x

13

Thus, 5(1) is the get-go chemical element of vector v, v(two) its 2d element, and and then forth. Furthermore, to access blocks of elements, we use MATLAB's colon notation (:). For example, to access the get-go three elements of v, we write,

>> v(ane:3)

ans = i 4 7

Or, all elements from the 3rd through the last elements,

>> five(iii,end)

ans = 7 10 thirteen

where terminate signifies the final element in the vector. If v is a vector, writing

>> 5(:)

produces a cavalcade vector, whereas writing

>> five(1:end)

produces a row vector.

Inbound a matrix

A matrix is an array of numbers. To type a matrix into MATLAB you must

• brainstorm with a square bracket, [

• dissever elements in a row with spaces or commas (,)

• utilize a semicolon (;) to dissever rows

• finish the matrix with another foursquare subclass, ].

Here is a typical example. To enter a matrix A, such equally,

type

>> A = [ane 2 3; 4 5 half-dozen; 7 8 9]

MATLAB then displays the 3 × 3 matrix as follows,

A = 1 2 3

iv v six

7 viii 9

Annotation that the use of semicolons (;) here is different from their use mentioned earlier to suppress output or to write multiple commands in a unmarried line.

One time we accept entered the matrix, it is automatically stored and remembered in the Workspace. We can refer to it simply as matrix A. We tin can and so view a particular element in a matrix by specifying its location. We write,

>> A(2,one)

ans = iv

A(ii,1) is an element located in the second row and get-go column. Its value is iv.

Matrix indexing

We select elements in a matrix simply as nosotros did for vectors, but now nosotros need two indices. The element of row i and column j of the matrix A is denoted by A(i,j). Thus, A(i,j) in MATLAB refers to the chemical element Aij of matrix A. The first index is the row number and the second index is the column number. For example, A(i,3) is an chemical element of starting time row and third column. Here, A(1,3)=3.

Correcting whatsoever entry is piece of cake through indexing. Hither we substitute A(3,3)=9 by A(3,3)=0. The result is

>> A(3,three) = 0

A = one 2 3

4 5 6

seven 8 0

Single elements of a matrix are accessed as A(i,j), where i ≥ 1 and j ≥ 1. Nothing or negative subscripts are not supported in MATLAB.

Colon operator

The colon operator will testify very useful and understanding how it works is the central to efficient and convenient usage of MATLAB. It occurs in several different forms.

Often we must deal with matrices or vectors that are also large to enter one element at a fourth dimension. For example, suppose nosotros want to enter a vector x consisting of points (0, 0.i, 0.2, 0.3, · · · , five). We can use the command

>> x = 0:0.1:5;

The row vector has 51 elements

Linear spacing

On the other manus, there is a control to generate linearly spaced vectors: linspace. Information technology is similar to the colon operator (:), but gives direct control over the number of points. For case,

y = linspace(a,b)

generates a row vector y of 100 points linearly spaced between and including a and b.

y = linspace(a,b,n)

generates a row vector y of northward points linearly spaced betwixt and including a and b. This is useful when we want to divide an interval into a number of subintervals of the same length. For example,

>> theta = linspace(0,2*pi,101)

divides the interval [0, 2π] into 100 equal subintervals, so creating a vector of 101 elements.

Colon operator in a matrix

The colon operator can also be used to pick out a certain row or column. For example, the statement A(m:n,thou:l specifies rows m to northward and column k to l. Subscript expressions refer to portions of a matrix. For example,

>> A(ii,:)

ans = 4 five 6

is the second row elements of A.

The colon operator tin can also exist used to excerpt a sub-matrix from a matrix A.

>> A(:,2:3)

ans = two 3

5 6

eight 0

A(:,2:iii) is a sub-matrix with the concluding ii columns of A.

A row or a column of a matrix can be deleted by setting it to a null vector, [ ].

>> A(:,2)=[]

ans = 1 3

four vi

7 0

Creating a sub-matrix

To extract a submatrix B consisting of rows 2 and 3 and columns 1 and two of the matrix A, do the following

>> B = A([ii 3],[1 2])

B = 4 v

7 viii

To interchange rows 1 and two of A, utilize the vector of row indices together with the colon operator.

>> C = A([two 1 iii],:)

C = 4 5 half-dozen

i 2 3

seven eight 0

It is important to notation that the colon operator (:) stands for all columns or all rows. To create a vector version of matrix A, exercise the following

>> A(:)

ans = ane

2

iii

4

5

6

vii

viii

0

The submatrix comprising the intersection of rows p to q and columns r to s is denoted by A(p:q,r:s).

As a special instance, a colon (:) equally the row or cavalcade specifier covers all entries in that row or column; thus

• A(:,j) is the jth column of A, while

• A(i,:) is the ith row, and

• A(finish,:) picks out the terminal row of A.

>> A

A = 1 2 3

4 5 6

7 8 9

>> A(two:3,2:3)

ans = v 6

8 9

>> A([one 3],[2 iii])

ans = 2 iii

viii 9

Deleting row or cavalcade

To delete a row or column of a matrix, use the empty vector operator, [ ].

>> A(iii,:) = []

A = 1 2 three

four 5 half-dozen

Third row of matrix A is now deleted. To restore the third row, we apply a technique for creating a matrix Ezoic study this advert

>> A = [A(1,:);A(2,:);[7 viii 0]]

A = 1 ii iii

4 5 6

7 viii 0

Matrix A is at present restored to its original form

Dimension

To determine the dimensions of a matrix or vector, use the command size. For example,

>> size(A)

ans = iii 3

means 3 rows and 3 columns.

Continuation

If it is not possible to type the unabridged input on the aforementioned line, use sequent periods, called an ellipsis . . ., to signal continuation, then go along the input on the next line.

Notation that blank spaces around +, −, = signs are optional, but they meliorate readability.

Transposing a matrix

The transpose operation is denoted by an apostrophe or a unmarried quote ('). Information technology flips a matrix nearly its main diagonal and it turns a row vector into a column vector. Thus,

>> A'

ans = 1 4 7

2 5 eight

3 6 0

By using linear algebra annotation, the transpose of m × due north real matrix A is the n × m matrix that results from interchanging the rows and columns of A. The transpose matrix is denoted A^T .

Matrix generators

MATLAB provides functions that generates unproblematic matrices. The matrix of zeros, the matrix of ones, and the identity matrix are returned by the functions zeros, ones, and center, respectively.

For a complete list of uncomplicated matrices and matrix manipulations, type assist elmat or doctor elmat. Hither are some examples:

>> b=ones(iii,1)

b = ane

ane

ane

Equivalently, we can ascertain b as >> b=[i;1;1]

>> eye(3)

ans = 1 0 0

0 1 0

0 0 one

In add-on, it is important to recall that the iii elementary operations of improver (+), subtraction (−), and multiplication (∗) apply also to matrices whenever the dimensions are compatible.

Two other important matrix generation functions are rand and randn, which generate matrices of (pseudo-)random numbers using the aforementioned syntax equally middle.

In addition, matrices tin be synthetic in a block form. With C defined by C = [1 ii; 3 iv], we may create a matrix D equally follows

>> D = [C zeros(two); ones(2) heart(ii)]

D = one 2 0 0

3 4 0 0

one i ane 0

1 1 0 ane

Special matrices

MATLAB provides a number of special matrices (come across Table two.5). These matrices accept interesting properties that brand them useful for constructing examples and for testing algorithms. For more than information, run across MATLAB documentation.