Constructing Matrices
| Table[f,{i,m},{j,n}] | build an m×n matrix where f is a function of i and j that gives the value of the   entry |
| Array[f,{m,n}] | build an m×n matrix whose   entry is  |
| ConstantArray[a,{m,n}] | build an m×n matrix with all entries equal to a |
| DiagonalMatrix[list] | generate a diagonal matrix with the elements of list on the diagonal |
| IdentityMatrix[n] | generate an n×n identity matrix |
| Normal[SparseArray[{{i1,j1}->v1,{i2,j2}->v2,...},{m,n}]] | make a matrix with nonzero values  at positions  |
Functions for constructing matrices.
This generates a 2×2 matrix whose
entry is
.
| Out[1]= |  |
Here is another way to produce the same matrix.
| Out[2]= |  |
This creates a 3×2 matrix of zeros.
| Out[3]= |  |
DiagonalMatrix makes a matrix with zeros everywhere except on the leading diagonal.
| Out[4]= |  |
| Out[5]= |  |
This makes a 3×4 matrix with two nonzero values filled in.
| Out[6]= |  |
MatrixForm prints the matrix in a two-dimensional form.
Out[7]//MatrixForm= |
| |  |
| Table[0,{m},{n}] | a matrix of zeros |
| Table[If[i>=j,1,0],{i,m},{j,n}] | a lower-triangular matrix |
| RandomReal[{0,1},{m,n}] | a matrix with random numerical entries |
Constructing special types of matrices.
Table evaluates
If[i≥j, a++, 0] separately for each element, to give a matrix with sequentially increasing entries in the lower-triangular part.
| Out[8]= |  |
Constructing special types of matrices with SparseArray.
This sets up a general lower-triangular matrix.
Out[9]//MatrixForm= |
| |  |
