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Det
Det[
m
] gives the determinant of the square matrix m.
Det[
m
,
Modulus->
n
] computes the determinant modulo n.
See the Mathematica book: Section 1.8.3, Section 3.7.7.
See also Implementation NotesA.9.44.27MainBookLinkOldButtonDataA.9.44.27, Implementation NotesA.9.44.29MainBookLinkOldButtonDataA.9.44.29.
See also: Minors, RowReduce, NullSpace, Signature.
Further Examples
This is the determinant of a  x  matrix.
In[1]:= 
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This is the determinant of the same matrix over the integers modulo 9.
In[2]:= 
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This is the determinant of a 15 x 15 matrix.
In[3]:= 
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This genarates a randomly generated 20 x 20 matrix and times how long that takes. The coefficients of the matrix have 50 digits of precision, and lie in the region of the complex plane defined by -10
<
Re(z)
<
10, -10
<
Im(z)
<
10.
In[4]:= 
In[5]:= 
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This computes the determinant of the matrix and again times the calculation.
In[6]:= 
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In[7]:= 
This is a different type of matrix. The entries are Gaussian integers with real and imaginary parts between  and  .
In[8]:= 
Here is its determinant and how long it takes to calculate it.
In[9]:= 
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In[10]:= 
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