Creating Matrixes in Matlab
Matlab Define Row and Column Vectors (Matrix)
% A column vector 4 by 1, with three numbers you fill in by yourself
colVec = [5;2;3;10]
% Another column vector with 4 random numbers
colVecRand = rand(4,1)
% A row vector 1 by 4
rowVec = [3,2,4,5]
% A row vector 1 by 4 with random number
rowVecRand = rand(1,4)
Matlab Define a Matrix
% A 2 by 3 matrix by hand
matA = [1,2,1;
3,4,10]
% Another 2 by 3 matrix, now with random numbers
matRand = rand(2,3)
% Another 2 by 3 matrix, now with random integers between 1 and 10
% rand draws between 0 and 1, ceil converts 0.1 to 1, 1.1 to 2, etc
matRand = ceil(rand(2,3)*10)
Matlab Define a Square Matrix
% A 4 by 4 square matrix
matSquare = rand(4)
% or can define 4 by 4
matSquare = rand(4, 4)
% or can define 4 by 4, between 1 and 5 each number
matSquare = ceil(rand(4, 4)*5)
Identity Matrix
If a matrix A is square matrix with the same number of rows and columns, and all diagonal elements are 1 and non-diagonal elements are 0, then A is an identity matrix:
are the value in the ith row and jth column of the matrix A- A is an identity matrix, when:
, 
% 4 by 4 identity matrix
identity4by4 = eye(4)
When a matrix is muplieid by the identity matrix, you get the same matrix back, for example, multiplying random integer 4 by 4 matrix by the 4 by 4 identity matrix:
matSquare
matSquareTimesIdentity = matSquare*identity4by4
When a row vector is muplieid by the identity matrix, you get the same vector back, for example, multiplying random integer 1 by 4 row vector by the 4 by 4 identity matrix:
rowVec
rowVecTimesIdentity = rowVec*identity4by4
When an identity matrix is multiplied by a column vector, you get the same vector back, for example, multiplying 4 by 4 identity matrix by random integer 4 by 1 column vector by the :
colVec
colVecTimesIdentity = identity4by4*colVec
Lower-Triangular Matrix and Upper-Triangular Matrix
A lower triangular matrix is a square matrix where:
- Square matrixA is a lower triangular matrix, when:
- Square matrixA is a upper triangular matrix, when:
% lower triangular matrix of matA
lowerTriangular = tril(matSquare)
% upper triangular matrix of matA
upperTriangular = triu(matSquare)
Three Dimensions Matrix (Tensor)
% 3 by 3 by 2, storing multiple matrixes together in tenA
tenA = zeros(3,3,2);
tenA(:,:,1) = rand(3,3);
tenA(:,:,2) = rand(3,3);
disp(tenA);
% Creating four 2 by 3 matrixes
matRand = rand(2,3,4)
disp(matRand);