# GLKMatrix3 ## Overview The `GLKMatrix3` type defines a `3x3` floating-point matrix as well as many mathematical operations commonly used to manipulate matrices. A `3x3` matrix is commonly used in graphics programming to represent scaling or rotation transformations to convert from one coordinate system to another. The functions that manipulate `GLKMatrix3` structures treat the inputs as immutable, instead returning a new matrix that represent the results of the operation. ## Topics ### Creating Matrices [`func GLKMatrix3Make(Float, Float, Float, Float, Float, Float, Float, Float, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3Make(_:_:_:_:_:_:_:_:_:)) Returns a `3x3` matrix created from individual component values. [`func GLKMatrix3MakeAndTranspose(Float, Float, Float, Float, Float, Float, Float, Float, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeAndTranspose(_:_:_:_:_:_:_:_:_:)) Returns a `3x3` transposed matrix created from individual component values. [`func GLKMatrix3MakeWithArray(UnsafeMutablePointer!) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeWithArray(_:)) Returns a `3x3` matrix created from an array of component values. [`func GLKMatrix3MakeWithArrayAndTranspose(UnsafeMutablePointer!) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeWithArrayAndTranspose(_:)) Returns a `3x3` transposed matrix created from an array of component values. [`func GLKMatrix3MakeWithColumns(GLKVector3, GLKVector3, GLKVector3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeWithColumns(_:_:_:)) Returns a `3x3` matrix created from three column vectors. [`func GLKMatrix3MakeWithRows(GLKVector3, GLKVector3, GLKVector3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeWithRows(_:_:_:)) Returns a `3x3` matrix created from three row vectors. [`func GLKMatrix3MakeRotation(Float, Float, Float, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeRotation(_:_:_:_:)) Returns a `3x3` matrix that performs a rotation around an arbitrary vector. [`func GLKMatrix3MakeXRotation(Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeXRotation(_:)) Returns a `3x3` matrix that performs a rotation around the positive x-axis. [`func GLKMatrix3MakeYRotation(Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeYRotation(_:)) Returns a `3x3` matrix that performs a rotation around the positive y-axis. [`func GLKMatrix3MakeZRotation(Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeZRotation(_:)) Returns a `3x3` matrix that performs a rotation around the positive z-axis. [`func GLKMatrix3MakeWithQuaternion(GLKQuaternion) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeWithQuaternion(_:)) Returns a `3x3` matrix that performs a rotation based on a quaternion. [`func GLKMatrix3MakeScale(Float, Float, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3MakeScale(_:_:_:)) Returns a `3x3` matrix that performs a scaling transformation. ### Working With Parts of a Matrix [`func GLKMatrix3GetMatrix2(GLKMatrix3) -> GLKMatrix2`](/documentation/GLKit/GLKMatrix3GetMatrix2(_:)) Returns the upper-left `2x2` section of a `3x3` matrix. [`func GLKMatrix3GetColumn(GLKMatrix3, Int32) -> GLKVector3`](/documentation/GLKit/GLKMatrix3GetColumn(_:_:)) Retrieves a column from a `3x3` matrix. [`func GLKMatrix3GetRow(GLKMatrix3, Int32) -> GLKVector3`](/documentation/GLKit/GLKMatrix3GetRow(_:_:)) Retrieves a row from a `3x3` matrix. [`func GLKMatrix3SetColumn(GLKMatrix3, Int32, GLKVector3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3SetColumn(_:_:_:)) Returns a new `3x3` matrix with one column replaced by a new vector. [`func GLKMatrix3SetRow(GLKMatrix3, Int32, GLKVector3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3SetRow(_:_:_:)) Returns a new `3x3` matrix with one row replaced by a new vector. ### Performing Mathematical Operations on Matrices [`func GLKMatrix3Invert(GLKMatrix3, UnsafeMutablePointer!) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3Invert(_:_:)) Returns the inverse of a matrix. [`func GLKMatrix3Transpose(GLKMatrix3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3Transpose(_:)) Returns the transpose of a matrix. [`func GLKMatrix3InvertAndTranspose(GLKMatrix3, UnsafeMutablePointer!) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3InvertAndTranspose(_:_:)) Returns the inverse transpose of a matrix. [`func GLKMatrix3Multiply(GLKMatrix3, GLKMatrix3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3Multiply(_:_:)) Returns the product of two matrices. [`func GLKMatrix3Rotate(GLKMatrix3, Float, Float, Float, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3Rotate(_:_:_:_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a rotation around a vector. [`func GLKMatrix3RotateWithVector3(GLKMatrix3, Float, GLKVector3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3RotateWithVector3(_:_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a rotation around a vector. [`func GLKMatrix3RotateWithVector4(GLKMatrix3, Float, GLKVector4) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3RotateWithVector4(_:_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a rotation around a vector. [`func GLKMatrix3RotateX(GLKMatrix3, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3RotateX(_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a rotation around the x-axis. [`func GLKMatrix3RotateY(GLKMatrix3, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3RotateY(_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a rotation around the y-axis. [`func GLKMatrix3RotateZ(GLKMatrix3, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3RotateZ(_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a rotation around the z-axis. [`func GLKMatrix3Scale(GLKMatrix3, Float, Float, Float) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3Scale(_:_:_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a scaling transform. [`func GLKMatrix3ScaleWithVector3(GLKMatrix3, GLKVector3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3ScaleWithVector3(_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a scaling transform defined by a vector. [`func GLKMatrix3ScaleWithVector4(GLKMatrix3, GLKVector4) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3ScaleWithVector4(_:_:)) Returns a new `3x3` matrix created by concatenating a matrix with a scaling transform defined by a vector. [`func GLKMatrix3Add(GLKMatrix3, GLKMatrix3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3Add(_:_:)) Returns a new `3x3` matrix created by performing a component-wise addition of two matrices. [`func GLKMatrix3Subtract(GLKMatrix3, GLKMatrix3) -> GLKMatrix3`](/documentation/GLKit/GLKMatrix3Subtract(_:_:)) Returns a new `3x3` matrix created by performing a component-wise subtraction of two matrices. ### Performing Mathematical Operations on Vectors [`func GLKMatrix3MultiplyVector3(GLKMatrix3, GLKVector3) -> GLKVector3`](/documentation/GLKit/GLKMatrix3MultiplyVector3(_:_:)) Multiplies a `3x3` matrix by a vector. [`func GLKMatrix3MultiplyVector3Array(GLKMatrix3, UnsafeMutablePointer, Int)`](/documentation/GLKit/GLKMatrix3MultiplyVector3Array(_:_:_:)) Multiplies a `3x3` matrix by an array of vectors. ### Data Types [`typealias GLKMatrix2`](/documentation/GLKit/GLKMatrix2) A `2x2` matrix. [`typealias GLKMatrix3`](/documentation/GLKit/GLKMatrix3) A `3x3` matrix stored in column-major order. ### Constants [`let GLKMatrix3Identity: GLKMatrix3`](/documentation/GLKit/GLKMatrix3Identity) A `3x3` identity matrix. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)