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<BLOCKQUOTE>
<H1><A NAME="NAME"><A NAME="1">NAME
</A></A></H1>
<P>
<B>determinant</B> - returns the scalar determinant of a square matrix
</P>
<H1><A NAME="SYNOPSIS"><A NAME="2">SYNOPSIS
</A></A></H1>
<PRE> float determinant(float1x1 A);
float determinant(float2x2 A);
float determinant(float3x3 A);
float determinant(float4x4 A);
</PRE>
<H1><A NAME="PARAMETERS"><A NAME="3">PARAMETERS
</A></A></H1>
<DL>
<DT><STRONG>A
</STRONG></DT>
<DD>
<P>
Square matrix of which to compute the determinant.
</P>
</DD></DL>
<H1><A NAME="DESCRIPTION"><A NAME="4">DESCRIPTION
</A></A></H1>
<P>
Returns the determinant of the square matrix <I>A</I>.
</P>
<H1><A NAME="REFERENCE_IMPLEMENTATION"><A NAME="5">REFERENCE IMPLEMENTATION
</A></A></H1>
<P>
The various <B>determinant</B> functions can be implemented like this:
</P>
<PRE> float determinant(float1x1 A)
{
return A._m00;
}
float determinant(float2x2 A)
{
return A._m00*A._m11 - A._m01*A._m10;
}
float determinant(float3x3 A)
{
return dot(A._m00_m01_m02,
A._m11_m12_m10 * A._m22_m20_m21
- A._m12_m10_m11 * A._m21_m22_m20);
}
float determinant(float4x4 A) {
return dot(float4(1,-1,1,-1) * A._m00_m01_m02_m03,
A._m11_m12_m13_m10*( A._m22_m23_m20_m21*A._m33_m30_m31_m32
- A._m23_m20_m21_m22*A._m32_m33_m30_m31)
+ A._m12_m13_m10_m11*( A._m23_m20_m21_m22*A._m31_m32_m33_m30
- A._m21_m22_m23_m20*A._m33_m30_m31_m32)
+ A._m13_m10_m11_m12*( A._m21_m22_m23_m20*A._m32_m33_m30_m31
- A._m22_m23_m20_m21*A._m31_m32_m33_m30));
}
</PRE>
<H1><A NAME="PROFILE_SUPPORT"><A NAME="6">PROFILE SUPPORT
</A></A></H1>
<P>
<B>determinant</B> is supported in all profiles. However profiles such as
<A HREF="fp20.html">fp20</A> and <A HREF="ps_2_0.html">ps_2_0</A> without native floating-point will have problems
computing the larger determinants and may have ranges issues computing
even small determinants.
</P>
<H1><A NAME="SEE_ALSO"><A NAME="7">SEE ALSO
</A></A></H1>
<P>
<A HREF="mul.html">mul</A>, <A HREF="transpose.html">transpose</A>
</P>
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