Wolfram Language Fast Introduction for Math Students
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Matrices & Linear Algebra

The Wolfram Language represents matrices as lists of lists:

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⨯ 
{{1, 2}, {3, 4}}

Enter a table using CTRL+ ENTER for rows and CTRL+ , for columns:

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⨯ 
{
 {a, b},
 {c, d}
}
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MatrixForm displays output as a matrix:

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⨯ 
MatrixForm[{{a, b}, {c, d}}]
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You can construct a matrix with iterative functions:

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⨯ 
Table[x + y, {x, 1, 3}, {y, 0, 2}]
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Or import data that represents a matrix:

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⨯ 
Import["data.csv"]
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IdentityMatrix, DiagonalMatrix and others are built-in symbols.

Standard matrix operations work elementwise:

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⨯ 
{1, 2, 3} {a, b, c}
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Compute the dot product of two matrices:

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⨯ 
{{1, 2}, {3, 4}}.{{a, b}, {c, d}}
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Find the determinant:

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⨯ 
Det[{{a, b}, {c, d}}]
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Get the inverse of a matrix:

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⨯ 
Inverse[{{1, 1}, {0, 1}}]
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Use LinearSolve to solve a linear system:

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⨯ 
LinearSolve[{{1, 1}, {0, 1}}, {x, y}]
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Functions for minimization and matrix decomposition are available as well.

QUICK REFERENCE: Matrices and Linear Algebra »