◆ Determinant()

Fxp SRL::Math::Types::Matrix33::Determinant ( ) const

inlineconstexprinherited

Calculate the determinant of the matrix.

Computes the determinant using the Laplace expansion along the first row. The determinant is a scalar value that represents the scaling factor of the transformation represented by this matrix.

For a 3x3 matrix: | a b c | | d e f | | g h i |

det = a(ei-fh) - b(di-fg) + c(dh-eg)

Returns: The determinant value.

Note

Properties of the determinant:

det = 0 indicates a singular (non-invertible) matrix
det = 1 for pure rotation matrices
|det| represents the scale factor of the transformation

Matrix33 rotation = Matrix33::CreateRotationX(Angle::FromDegrees(90));

Fxp det = rotation.Determinant(); // Should be close to 1

SRL::Math::Types::Angle::FromDegrees

static consteval Angle FromDegrees(double degrees)

Creates angle from degrees at compile time.

Definition angle.hpp:204

SRL::Math::Types::Fxp

Fixed-point arithmetic optimized for Saturn hardware.

Definition fxp.hpp:57

SRL::Math::Types::Matrix33::Determinant

constexpr Fxp Determinant() const

Calculate the determinant of the matrix.

Definition mat33.hpp:606

SRL::Math::Types::Matrix33::CreateRotationX

static constexpr Matrix33 CreateRotationX(const Angle &angle)

Create a new X-axis rotation matrix.

Definition mat33.hpp:321

SRL::Math::Types::Matrix33::Matrix33

constexpr Matrix33()

Default constructor initializing to a zero matrix.

Definition mat33.hpp:76