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 :
A ij 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.
v i 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.
R n 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)
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