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  UNDER CONSTRUCTION

MATLAB:
Linear Algebra




Matrix basics

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

# , separates elements, ; separates rows

v = [1;2;3] 
[m,n] = size(A)

dim_A = size(A)
A_23 = A(2,3)
I = eye(3)
A_trans = A'
A_inv = inv(A)

% defines a 3x1 vector % gets dimensions of matrix A, storing them in % m = rows, n = columns % can also store in a variable % stores element in row 2, column 3 into A_23 % defines a 3x3 identity matrix % takes transpose of A % takes inverse of A

>> x = zeros(2, 4)
x =
     0   0   0   0
     0   0   0   0
	 
>> x = A(2, 1)
x =
    1.60
	
>> x = B(end, 2)
x =
    5.30

>> x = B(2,end-2)
x =
    6.11
	
>> x = B(:,2)
x =
    4.72
    9.07
    5.30

% generates a 2x4 matrix of zeros % extracts value of element in row 2, column 1 % extracts value of element in last row and column 2 % extracts value of element in row 2 and col. (last-2) % creates col. vector specifying all elements in col. 2

>> x = B([1 3],:)
x =
     3.00   4.72   0.00
     2.54   5.30   4.45

>> A(1,1) = 5.00
A
A =
     5.00   1.52
     1.60   3.63
	 
>> [Max, iMax] = max(v)
Max = 
   6.67
iMax = 
   2
   
>> max(max(B))
ans = 
     9.07
	 
>> A(:)
A =
     0.86   
     1.60
     1.52	 
     3.63

% creates matrix with all elements in rows 1 % and 3 of mtx. A % assigns value 5.00 to element in row 1 col. 1 % of mtx. A % finds max value of input vector, and its index; % stores value in Max, index in iMax % returns max value of entire matrix % put all elements of mtx. A in a single column, % sorted top-down left-right

>> B = [B, [1; 2; 3]]
B =
     3.00   4.72   0.00   1
     6.11   9.07   2.87   2
     2.54   5.30   4.45   3

% appends a column to the right of mtx. B



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