# Matrix Structure

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Represents a 3x3 affine transformation matrix used for transformations in two-dimensional space.

**Namespace:** System.Windows.Media

**Assembly:** System.Windows (in System.Windows.dll)

## Syntax

```
'Declaration
Public Structure Matrix _
Implements IFormattable
```

```
public struct Matrix : IFormattable
```

```
<Matrix .../>
```

```
<object property="m11,m12,m21,m22,offsetX,offsetY"/>
- or -
<object property="m11 m12 m21 m22 offsetX offsetY"/>
-or-
<object property="Identity"/>
```

#### XAML Values

*m11*

The numeric value in the first row and first column of this Matrix. For more information, see M11.*m12*

The numeric value in the first row and second column. For more information, see M12.*m21*

The numeric value in the second row and first column. For more information, see M21.*m22*

The numeric value in the second row and second column. For more information, see M22.*offsetX*

The numeric value in the third row and first column. For more information, see OffsetX.*offsetY*

The numeric value in the third row and second column. For more information, see OffsetY.Identity

The literal Identity value. See Identity.

The Matrix type exposes the following members.

## Properties

Name | Description | |
---|---|---|

Identity | Gets an identity Matrix. | |

IsIdentity | Gets a value that indicates whether this Matrix structure is an identity matrix. | |

M11 | Gets or sets the value of the first row and first column of this Matrix structure. | |

M12 | Gets or sets the value of the first row and second column of this Matrix structure. | |

M21 | Gets or sets the value of the second row and first column of this Matrix structure. | |

M22 | Gets or sets the value of the second row and second column of this Matrix structure. | |

OffsetX | Gets or sets the value of the third row and first column of this Matrix structure. | |

OffsetY | Gets or sets the value of the third row and second column of this Matrix structure. |

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## Methods

Name | Description | |
---|---|---|

Equals(Matrix) | Determines whether the specified Matrix structure is identical to this instance. | |

Equals(Object) | Determines whether the specified Object is a Matrix structure that is identical to this Matrix. (Overrides ValueType.Equals(Object).) | |

Finalize | Allows an object to try to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection. (Inherited from Object.) | |

GetHashCode | Returns the hash code for this Matrix structure. (Overrides ValueType.GetHashCode().) | |

GetType | Gets the Type of the current instance. (Inherited from Object.) | |

MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |

ToString() | Creates a String representation of this Matrix structure. (Overrides ValueType.ToString().) | |

ToString(IFormatProvider) | Creates a String representation of this Matrix structure with culture-specific formatting information. | |

Transform | Transforms the specified point by the Matrix and returns the result. |

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## Operators

Name | Description | |
---|---|---|

Equality | Determines whether the two specified Matrix structures are identical. | |

Inequality | Determines whether the two specified Matrix structures are not identical. |

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## Explicit Interface Implementations

Name | Description | |
---|---|---|

IFormattable.ToString | Infrastructure. For a description of this member, see ToString. |

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## Remarks

A 3x3 matrix is used for transformations in a two-dimensional x-y plane. Affine transformation matrices can be multiplied to form any number of linear transformations, such as rotation and skew (shear), followed by translation. An affine transformation matrix has its final column equal to (0, 0, 1), so only the members in the first two columns need to be specified. Note that vectors are expressed as row-vectors, not column vectors.

A Matrix is stored using row-major order and has the following structure:

The members in the last row, OffsetX and OffsetY, represent translation values.

In methods and properties, the transformation matrix is usually specified as a vector with only six members, as follows:

(M11, M12, M21, M22, OffsetX, OffsetY)

Although you can use a Matrix structure directly to translate individual points, or with a MatrixTransform to transform objects, Silverlight also provides a set of classes that enable you to transform objects without working directly with matrices: RotateTransform, ScaleTransform, SkewTransform, and TranslateTransform.

Properties of a Matrix are animatable (as one or more DoubleAnimation animations or DoubleAnimationUsingKeyFrames).

A Matrix provides the property value for the MatrixTransform.Matrix property.

Related types can be used for transformation matrices in three-dimensional space and then used for a projection. See Matrix3D and Matrix3DProjection.

In the XAML syntax, either a comma or space can be used as a delimiter.

## Examples

The following XAML defines a Matrix that provides data for a MatrixTransform applied to a rectangular shape. In this case, the matrix combines an offset (OffsetX and OffsetY) and a skew (M12). Note that this same effect could have been produced by combining a TranslateTransform and a SkewTransform. Whether to use a single Matrix or combinations of discrete transforms is a matter of coding style, the results are identical.

## Version Information

#### Silverlight

Supported in: 5, 4, 3

#### Silverlight for Windows Phone

Supported in: Windows Phone OS 7.1, Windows Phone OS 7.0

## Platforms

For a list of the operating systems and browsers that are supported by Silverlight, see Supported Operating Systems and Browsers.

## Thread Safety

Any public static (Shared in Visual Basic) members of this type are thread safe. Any instance members are not guaranteed to be thread safe.