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perazz committed Jan 31, 2025
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### Notes

- This function relies on LAPACK's least-squares solvers, such as [`*GELSS`](@ref la_lapack::gelss).
- This function relies on LAPACK's least-squares solvers, such as [GELSS](@ref la_lapack::gelss).
- If `overwrite_a` is enabled, the original contents of `a` and `b` may be lost.

## [det](@ref la_linalg::det) - Determinant of a scalar or rectangular matrix.
## [det](@ref la_determinant::det) - Determinant of a scalar or rectangular matrix.

### Syntax

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### Return value

The function returns a scalar value representing the determinant of the input matrix \f$ A \f$. The return type is the same as the input matrix (real precision).
The function returns a `real` scalar value representing the determinant of the input matrix \f$ A \f$, with the same kind as \f$ A \f$.

### Errors

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### Notes

- This operator internally calls [pinv](@ref la_pseudoinverse::pinv) and behaves identically.
- The pseudo-inverse is computed using LAPACK’s SVD decomposition routine [`*GESVD`](@ref la_lapack::gesvd).
- The pseudo-inverse is computed using LAPACK’s SVD decomposition routine [GESVD](@ref la_lapack::gesvd).
- This operator is a convenient shorthand for calling the functional interface `pinv(a)`.


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- `a`: A `real` or `complex` matrix of size \f$ [m,n] \f$, representing the coefficient matrix. If `overwrite_a = .false.`, this is an input argument. If `overwrite_a = .true.`, it is an `inout` argument and is overwritten upon return.
- `q`: A rank-2 array of the same type and kind as `a`, representing the orthonormal matrix \f$ Q \f$. This is an output argument with shape \f$ [m,m] \f$ (for the full problem) or \f$ [m,k] \f$ (for the reduced problem).
- `r`: A rank-2 array of the same type and kind as `a`, representing the upper-triangular matrix \f$ R \f$. This is an output argument with shape \f$ [m,n] \f$ (for the full problem) or \f$ [k,n] \f$ (for the reduced problem).
- `storage` (optional): A rank-1 array of the same type and kind as `a`, providing working storage for the solver. Its minimum size can be determined by a call to [`qr_space`](@ref la_qr::qr_space). This is an output argument.
- `storage` (optional): A rank-1 array of the same type and kind as `a`, providing working storage for the solver. Its minimum size can be determined by a call to [qr_space](@ref la_qr::qr_space). This is an output argument.
- `overwrite_a` (optional, default = `.false.`): A logical flag that determines whether the input matrix `a` can be overwritten. If `.true.`, the matrix `a` is used as temporary storage and overwritten to avoid internal memory allocation. This is an input argument.
- `err` (optional): A [type(la_state)](@ref la_state_type::la_state) variable that returns the error state. If not provided, the function will stop execution on error.

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