# MatCreateCentering
Creates a new matrix object that implements the (symmetric and idempotent) centering matrix, I - (1/N) * ones*ones' 
## Synopsis
```
#include "petscmat.h" 
PetscErrorCode MatCreateCentering(MPI_Comm comm, PetscInt n, PetscInt N, Mat *C)
```
Collective


## Input Parameters

- ***comm -*** MPI communicator
- ***n -*** number of local rows (or `PETSC_DECIDE` to have calculated if N is given)
This value should be the same as the local size used in creating the
y vector for the matrix-vector product y = Ax.
- ***N -*** number of global rows (or `PETSC_DETERMINE` to have calculated if n is given)



## Output Parameter

- ***C -*** the matrix



## Notes
The entries of the matrix C are not explicitly stored. Instead, the new matrix
object is a shell that simply performs the action of the centering matrix, i.e.,
multiplying C*x subtracts the mean of the vector x from each of its elements.
This is useful for preserving sparsity when mean-centering the columns of a
matrix is required. For instance, to perform principal components analysis with
a matrix A, the composite matrix C*A can be passed to a partial SVD solver.




## See Also
 `MatCreateLRC()`, `MatCreateComposite()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/centering/centering.c.html#MatCreateCentering">src/mat/impls/centering/centering.c</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/mat/impls/centering/centering.c)


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