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 i, jth entry |
| Array[f,{m,n}] | build an m×n matrix whose i, jth entry is f[i, j] |
| 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 non-zero values vk at positions {ik, jk} |
Functions for constructing matrices.
This generates a 2×2 matrix whose i, jth entry is a[i, j].
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Here is another way to produce the same matrix.
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This creates a 3×2 matrix of zeros.
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DiagonalMatrix makes a matrix with zeros everywhere except on the leading diagonal.
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This makes a 3×4 matrix with two non-zero values filled in.
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MatrixForm prints the matrix in a two-dimensional form.
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| 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.
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Constructing special types of matrices with SparseArray.
This sets up a general lower-triangular matrix.
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