The Inspector-executor Sparse BLAS API can perform several operations involving sparse matrices. These notations are used in the description of the operations:

• A, G, V are sparse matrices

• B and C are dense matrices

• x and y are dense vectors

• alpha and beta are scalars

op(A) represents a possible transposition of matrix A

• op(A) = A

• op(A) = AT - transpose of A

• op(A) = AH - conjugate transpose of A

op(A)-1 denotes the inverse of op(A).

The Inspector-executor Sparse BLAS routines support the following operations:

• computing the vector product between a sparse matrix and a dense vector:

`y := alpha*op(A)*x + beta*y`

• solving a single triangular system:

`y := alpha*inv(op(A))*x`

• computing a product between a sparse matrix and a dense matrix:

`C := alpha*op(A)*B + beta*C`

• computing a product between sparse matrices with a sparse result:
`V := alpha*op(A)*op(G)`
• computing a product between sparse matrices with a dense result:
`C := alpha*op(A)*op(G)`
• computing a sum of sparse matrices with a sparse result:
`V := alpha*op(A) + G`
• solving a sparse triangular system with multiple right-hand sides:

`C := alpha*inv(op(A))*B`