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# PetscDTAltVPullbackMatrix
Compute the pullback matrix for k-forms under a linear transformation 
## Synopsis
```
#include "petscdt.h" 
PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt N, PetscInt M, const PetscReal *L, PetscInt k, PetscReal *Lstar)
```

## Input Parameters

- ***N -*** the dimension of the origin vector space of the linear transformation, N >= 0
- ***M -*** the dimension of the image vector space of the linear transformation, M >= 0
- ***L -*** a linear transformation, an [M x N] matrix in row-major format
- ***k -*** the *signed* degree k of the |k|-forms on which Lstar acts, -(min(M,N)) <= k <= min(M,N).
A negative form degree indicates that the pullback should be conjugated by the Hodge star operator (see note in `PetscDTAltvPullback()`)



## Output Parameter

- ***Lstar -*** the pullback matrix, an [(N choose |k|) x (M choose |k|)] matrix in row-major format such that Lstar * w = L^* w





## See Also
 `PetscDTAltV`, `PetscDTAltVPullback()`, `PetscDTAltVStar()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/dm/dt/interface/dtaltv.c.html#PetscDTAltVPullbackMatrix">src/dm/dt/interface/dtaltv.c</A>


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