---
title: Matrices and Vectors
framework: metalperformanceshaders
role: collectionGroup
role_heading: API Collection
path: metalperformanceshaders/matrices-and-vectors
---

# Matrices and Vectors

Solve systems of equations, factorize matrices and multiply matrices and vectors.

## Topics

### Matrices

- [MPSMatrix](metalperformanceshaders/mpsmatrix.md)
- [MPSMatrixDescriptor](metalperformanceshaders/mpsmatrixdescriptor.md)
- [MPSTemporaryMatrix](metalperformanceshaders/mpstemporarymatrix.md)

### Vectors

- [MPSVector](metalperformanceshaders/mpsvector.md)
- [MPSVectorDescriptor](metalperformanceshaders/mpsvectordescriptor.md)
- [MPSTemporaryVector](metalperformanceshaders/mpstemporaryvector.md)

### Classes for Decomposition and Solving

- [MPSMatrixDecompositionCholesky](metalperformanceshaders/mpsmatrixdecompositioncholesky.md)
- [MPSMatrixSolveCholesky](metalperformanceshaders/mpsmatrixsolvecholesky.md)
- [MPSMatrixDecompositionLU](metalperformanceshaders/mpsmatrixdecompositionlu.md)
- [MPSMatrixSolveLU](metalperformanceshaders/mpsmatrixsolvelu.md)
- [MPSMatrixSolveTriangular](metalperformanceshaders/mpsmatrixsolvetriangular.md)
- [MPSMatrixUnaryKernel](metalperformanceshaders/mpsmatrixunarykernel.md)
- [MPSMatrixBinaryKernel](metalperformanceshaders/mpsmatrixbinarykernel.md)
- [MPSMatrixDecompositionStatus](metalperformanceshaders/mpsmatrixdecompositionstatus.md)

### Matrix Arithmetic Operations

- [MPSMatrixSum](metalperformanceshaders/mpsmatrixsum.md)
- [MPSMatrixMultiplication](metalperformanceshaders/mpsmatrixmultiplication.md)
- [MPSMatrixVectorMultiplication](metalperformanceshaders/mpsmatrixvectormultiplication.md)
- [MPSMatrixFindTopK](metalperformanceshaders/mpsmatrixfindtopk.md)

### Matrix Copying Operations

- [MPSMatrixCopy](metalperformanceshaders/mpsmatrixcopy.md)
- [MPSMatrixCopyToImage](metalperformanceshaders/mpsmatrixcopytoimage.md)
- [MPSMatrixCopyDescriptor](metalperformanceshaders/mpsmatrixcopydescriptor.md)
- [MPSImageCopyToMatrix](metalperformanceshaders/mpsimagecopytomatrix.md)

### Matrix Neural Network Operations

- [MPSMatrixFullyConnected](metalperformanceshaders/mpsmatrixfullyconnected.md)
- [MPSMatrixFullyConnectedGradient](metalperformanceshaders/mpsmatrixfullyconnectedgradient.md)
- [MPSMatrixNeuron](metalperformanceshaders/mpsmatrixneuron.md)
- [MPSMatrixNeuronGradient](metalperformanceshaders/mpsmatrixneurongradient.md)

### Matrix Softmax Operations

- [MPSMatrixLogSoftMax](metalperformanceshaders/mpsmatrixlogsoftmax.md)
- [MPSMatrixLogSoftMaxGradient](metalperformanceshaders/mpsmatrixlogsoftmaxgradient.md)
- [MPSMatrixSoftMax](metalperformanceshaders/mpsmatrixsoftmax.md)
- [MPSMatrixSoftMaxGradient](metalperformanceshaders/mpsmatrixsoftmaxgradient.md)

### Matrix Normalization Operations

- [MPSMatrixBatchNormalization](metalperformanceshaders/mpsmatrixbatchnormalization.md)
- [MPSMatrixBatchNormalizationGradient](metalperformanceshaders/mpsmatrixbatchnormalizationgradient.md)