02 Matrices And Vectors Instructionsl

02_matrices-and-vectors_instructionsl

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Matrices and Vectors

Matrices are 2-dimensional arrays:

a b c

d e f

g h i

j k l

The above matrix has four rows and three columns, so it is a 4 x 3 matrix.

A vector is a matrix with one column and many rows:

w

x

y

z

So vectors are a subset of matrices. The above vector is a 4 x 1 matrix.

Notation and terms :

Aij refers to the element in the ith row and jth column of matrix A.

A vector with 'n' rows is referred to as an 'n'-dimensional vector.

vi refers to the element in the ith row of the vector.

In general, all our vectors and matrices will be 1-indexed. Note that for

some programming languages, the arrays are 0-indexed.

Matrices are usually denoted by uppercase names while vectors are

lowercase.

"Scalar" means that an object is a single value, not a vector or matrix.

R refers to the set of scalar real numbers.

Rn refers to the set of n-dimensional vectors of real numbers.

Run the cell below to get familiar with the commands in Octave/Matlab. Feel free

to create matrices and vectors and try out different things.

% The ; denotes we are going back to a new row.

A = [1, 2, 3; 4, 5, 6; 7, 8, 9; 10, 11, 12]

[ ]

[ ]

% Initialize a vector

v = [1;2;3]

% Get the dimension of the matrix A where m = rows and n = columns

[m,n] = size(A)

% You could also store it this way

dim_A = size(A)

% Get the dimension of the vector v

dim_v = size(v)

% Now let's index into the 2nd row 3rd column of matrix A

A_23 = A(2,3)