# Matrix4x4 > A standard 4x4 transformation matrix. ## Definition * **Type:** Struct * **Namespace:** [UnityEngine](/engine/6000.7/script-reference/unityengine.md) * **Assembly:** UnityEngine.CoreModule * **Implements:** [IEquatable\](https://learn.microsoft.com/dotnet/api/system.iequatable-1), [IFormattable](https://learn.microsoft.com/dotnet/api/system.iformattable) ```csharp public struct Matrix4x4 : IEquatable, IFormattable ``` ## Remarks 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 [Vector3](/engine/6000.7/script-reference/unityengine/vector3.md)s, [Quaternion](/engine/6000.7/script-reference/unityengine/quaternion.md)s and functionality of [Transform](/engine/6000.7/script-reference/unityengine/transform.md) class is more straightforward. Plain matrices are used in special cases like setting up nonstandard camera projection. In Unity, several [Transform](/engine/6000.7/script-reference/unityengine/transform.md), [Camera](/engine/6000.7/script-reference/unityengine/camera.md), [Material](/engine/6000.7/script-reference/unityengine/material.md), [Graphics](/engine/6000.7/script-reference/unityengine/graphics.md) and [GL](/engine/6000.7/script-reference/unityengine/gl.md) functions use Matrix4x4. Matrices in Unity are column major; i.e. the position of a transformation matrix is in the last column, and the first three columns contain x, y, and z-axes. Data is accessed as: `row + (column*4)`. Matrices can be indexed like 2D arrays but note that in an expression like `mat[a, b]`, `a` refers to the row index, while `b` refers to the column index. ## Examples ```csharp using UnityEngine; public class ExampleScript : MonoBehaviour { void Start() { // get matrix from the Transform var matrix = transform.localToWorldMatrix; // get position from the last column var position = new Vector3(matrix[0,3], matrix[1,3], matrix[2,3]); Debug.Log("Transform position from matrix is: " + position); } } ``` ## Properties | Property | Description | | --------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------- | | [decomposeProjection](/engine/6000.7/script-reference/unityengine/matrix4x4/decomposeprojection.md) | This property takes a projection matrix and returns the six plane coordinates that define a projection frustum. | | [determinant](/engine/6000.7/script-reference/unityengine/matrix4x4/determinant.md) | The determinant of the matrix. (Read Only) | | [inverse](/engine/6000.7/script-reference/unityengine/matrix4x4/inverse.md) | The inverse of this matrix. (Read Only) | | [isIdentity](/engine/6000.7/script-reference/unityengine/matrix4x4/isidentity.md) | Checks whether this is an identity matrix. (Read Only) | | [this\[\]](/engine/6000.7/script-reference/unityengine/matrix4x4/item.md) | Access element at sequential index (0..15 inclusive). | | [lossyScale](/engine/6000.7/script-reference/unityengine/matrix4x4/lossyscale.md) | Attempts to get a scale value from the matrix. (Read Only) | | [rotation](/engine/6000.7/script-reference/unityengine/matrix4x4/rotation.md) | Attempts to get a rotation quaternion from this matrix. | | [transpose](/engine/6000.7/script-reference/unityengine/matrix4x4/transpose.md) | Returns the transpose of this matrix (Read Only). | ## Static Properties | Property | Description | | ----------------------------------------------------------------------------- | ----------------------------------------------------------- | | [identity](/engine/6000.7/script-reference/unityengine/matrix4x4/identity.md) | Returns the identity matrix (Read Only). | | [zero](/engine/6000.7/script-reference/unityengine/matrix4x4/zero.md) | Returns a matrix with all elements set to zero (Read Only). | ## Methods | Method | Description | | --------------------------------------------------------------------------------------------- | --------------------------------------------------------------- | | [GetColumn](/engine/6000.7/script-reference/unityengine/matrix4x4/getcolumn.md) | Get a column of the matrix. | | [GetPosition](/engine/6000.7/script-reference/unityengine/matrix4x4/getposition.md) | Get position vector from the matrix. | | [GetRow](/engine/6000.7/script-reference/unityengine/matrix4x4/getrow.md) | Returns a row of the matrix. | | [MultiplyPoint](/engine/6000.7/script-reference/unityengine/matrix4x4/multiplypoint.md) | Transforms a position by this matrix (generic). | | [MultiplyPoint3x4](/engine/6000.7/script-reference/unityengine/matrix4x4/multiplypoint3x4.md) | Transforms a position by this matrix (fast). | | [MultiplyVector](/engine/6000.7/script-reference/unityengine/matrix4x4/multiplyvector.md) | Transforms a direction by this matrix. | | [SetColumn](/engine/6000.7/script-reference/unityengine/matrix4x4/setcolumn.md) | Sets a column of the matrix. | | [SetRow](/engine/6000.7/script-reference/unityengine/matrix4x4/setrow.md) | Sets a row of the matrix. | | [SetTRS](/engine/6000.7/script-reference/unityengine/matrix4x4/settrs.md) | Sets this matrix to a translation, rotation and scaling matrix. | | [ToString](/engine/6000.7/script-reference/unityengine/matrix4x4/tostring.md) | Returns a formatted string for this matrix. | | [TransformPlane](/engine/6000.7/script-reference/unityengine/matrix4x4/transformplane.md) | Returns a plane that is transformed in space. | | [ValidTRS](/engine/6000.7/script-reference/unityengine/matrix4x4/validtrs.md) | Checks if this matrix is a valid transform matrix. | ## Static Methods | Method | Description | | ------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------ | | [Frustum](/engine/6000.7/script-reference/unityengine/matrix4x4/frustum.md) | This function returns a projection matrix with viewing frustum that has a near plane defined by the coordinates that were passed in. | | [Inverse3DAffine](/engine/6000.7/script-reference/unityengine/matrix4x4/inverse3daffine.md) | Computes the inverse of a 3D affine matrix. | | [LookAt](/engine/6000.7/script-reference/unityengine/matrix4x4/lookat.md) | Create a "look at" matrix. | | [Ortho](/engine/6000.7/script-reference/unityengine/matrix4x4/ortho.md) | Create an orthogonal projection matrix. | | [Perspective](/engine/6000.7/script-reference/unityengine/matrix4x4/perspective.md) | Create a perspective projection matrix. | | [Rotate](/engine/6000.7/script-reference/unityengine/matrix4x4/rotate.md) | Creates a rotation matrix. | | [Scale](/engine/6000.7/script-reference/unityengine/matrix4x4/scale.md) | Creates a scaling matrix. | | [Translate](/engine/6000.7/script-reference/unityengine/matrix4x4/translate.md) | Creates a translation matrix. | | [TRS](/engine/6000.7/script-reference/unityengine/matrix4x4/trs.md) | Creates a translation, rotation and scaling matrix. | ## Operators | Operator | Description | | ----------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------- | | [Matrix4x4](/engine/6000.7/script-reference/unityengine/matrix4x4/op-implicit.md) | Converts a [float4x4](/engine/6000.7/script-reference/unity/mathematics/float4x4.md) to a [Matrix4x4](/engine/6000.7/script-reference/unityengine/matrix4x4.md). | | [float4x4](/engine/6000.7/script-reference/unityengine/matrix4x4/op-implicit.md) | Converts a [Matrix4x4](/engine/6000.7/script-reference/unityengine/matrix4x4.md) to a [float4x4](/engine/6000.7/script-reference/unity/mathematics/float4x4.md). | | [operator \*](/engine/6000.7/script-reference/unityengine/matrix4x4/op-multiply.md) | Multiplies two matrices. |