A standard 4x4 transformation matrix.

A transformation matrix can perform arbitrary linear 3D transformations (i.e. translation, rotation, scale, shear etc.)
and perspective transformations using homogenous coordinates. You rarely use matrices in scripts; most
often using Vector3s, Quaternions and functionality of Transform class is more straightforward. Plain matrices are used in special cases
like setting up nonstandard camera projection.

Consult any graphics textbook for in depth explanation of transformation matrices.

In Unity, Matrix4x4 is used by several Transform, Camera, Material and GL functions.

Matrices in unity are column major. Data is accessed as: row + (column*4). Matrices can be
indexed like 2D arrays but in an expression like mat[a, b], `a`

refers to the row index, while `b`

refers
to the column index (note that this is the opposite way round to Cartesian coordinates).

identity | Returns the identity matrix (Read Only). |

zero | Returns a matrix with all elements set to zero (Read Only). |

decomposeProjection | This property takes a projection matrix and returns the six plane coordinates that define a projection frustum. |

determinant | The determinant of the matrix. |

inverse | The inverse of this matrix (Read Only). |

isIdentity | Is this the identity matrix? |

lossyScale | Attempts to get a scale value from the matrix. |

rotation | Attempts to get a rotation quaternion from this matrix. |

this[int,int] | Access element at [row, column]. |

transpose | Returns the transpose of this matrix (Read Only). |

GetColumn | Get a column of the matrix. |

GetRow | Returns a row of the matrix. |

MultiplyPoint | Transforms a position by this matrix (generic). |

MultiplyPoint3x4 | Transforms a position by this matrix (fast). |

MultiplyVector | Transforms a direction by this matrix. |

SetColumn | Sets a column of the matrix. |

SetRow | Sets a row of the matrix. |

SetTRS | Sets this matrix to a translation, rotation and scaling matrix. |

ToString | Returns a nicely formatted string for this matrix. |

TransformPlane | Returns a plane that is transformed in space. |

ValidTRS | Checks if this matrix is a valid transform matrix. |

Frustum | This function returns a projection matrix with viewing frustum that has a near plane defined by the coordinates that were passed in. |

LookAt | Given a source point, a target point, and an up vector, computes a transformation matrix that corresponds to a camera viewing the target from the source, such that the right-hand vector is perpendicular to the up vector. |

Ortho | Creates an orthogonal projection matrix. |

Perspective | Creates a perspective projection matrix. |

Rotate | Creates a rotation matrix. |

Scale | Creates a scaling matrix. |

Translate | Creates a translation matrix. |

TRS | Creates a translation, rotation and scaling matrix. |

operator * | Multiplies two matrices. |

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