Table is one of the core tools in Mathematica for generating data and matrices. It can create both numeric matrices and symbolic matrices, which makes it very flexible.

1. Basic syntax

Table[expr, {i, imax}]

• expr: an expression
• i: the loop variable
• imax: the upper limit of the loop

Example:

Table[i^2, {i, 5}]

Output:

{1, 4, 9, 16, 25}

2. Specify a starting value and step size

Table[expr, {i, imin, imax, step}]

Example:

Table[2 i, {i, 1, 5, 2}]

Output:

{2, 6, 10}

3. Generate a 2D matrix

To generate an n × m matrix, nest two loops:

Table[a[i, j], {i, n}, {j, m}]

Example:

Table[a[i, j], {i, 3}, {j, 3}] // MatrixForm

4. Symbolic matrix example

n = 4;
A = Table[a[i, j], {i, n}, {j, n}]
A // MatrixForm

With Table, you can build symbolic matrices of almost any structure, including upper triangular, lower triangular, and diagonal matrices.

5. Conditional matrix generation

Table can be combined with If or other conditions:

Table[If[i == j, 1, 0], {i, 4}, {j, 4}] // MatrixForm

This generates a 4×4 identity matrix.

贡献者: Junyuan He