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# MatCreateKAIJ
Creates a matrix of type `MATKAIJ` to be used for matrices of the following form .vb [I \otimes S + A \otimes T] .ve where .vb S is a dense (p \times q) matrix T is a dense (p \times q) matrix A is a `MATAIJ`  (n \times n) matrix I is the identity matrix .ve The resulting matrix is (np \times nq) 
## Synopsis
```
#include "petscmat.h" 
PetscErrorCode MatCreateKAIJ(Mat A, PetscInt p, PetscInt q, const PetscScalar S[], const PetscScalar T[], Mat *kaij)
```
`S` and `T` are always stored independently on all processes as `PetscScalar` arrays in column-major format.

Collective


## Input Parameters

- ***A -*** the `MATAIJ` matrix
- ***p -*** number of rows in `S` and `T`
- ***q -*** number of columns in `S` and `T`
- ***S -*** the `S` matrix (can be `NULL`), stored as a `PetscScalar` array (column-major)
- ***T -*** the `T` matrix (can be `NULL`), stored as a `PetscScalar` array (column-major)



## Output Parameter

- ***kaij -*** the new `MATKAIJ` matrix





## Notes
This function increases the reference count on the `MATAIJ` matrix, so the user is free to destroy the matrix if it is not needed.

Changes to the entries of the `MATAIJ` matrix will immediately affect the `MATKAIJ` matrix.


## Developer Note
In the `MATMPIKAIJ` case, the internal 'AIJ' and 'OAIJ' sequential KAIJ matrices are kept up to date by tracking the object state
of the AIJ matrix 'A' that describes the blockwise action of the `MATMPIKAIJ` matrix and, if the object state has changed, lazily
rebuilding 'AIJ' and 'OAIJ' just before executing operations with the `MATMPIKAIJ` matrix. If new types of operations are added,
routines implementing those must also ensure these are rebuilt when needed (by calling the internal MatKAIJ_build_AIJ_OAIJ() routine).


## See Also
 [](ch_matrices), `Mat`, `MatKAIJSetAIJ()`, `MatKAIJSetS()`, `MatKAIJSetT()`, `MatKAIJGetAIJ()`, `MatKAIJGetS()`, `MatKAIJGetT()`, `MATKAIJ`

## Level
advanced

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

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex74.c.html">src/ksp/ksp/tutorials/ex74.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex77.c.html">src/ksp/ksp/tutorials/ex77.c</A><BR>


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


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