Small typos

Author: lkdvos

docs/src/man/backends.md

@@ -152,7 +152,7 @@ For convenience, the construction above is also provided in a specialized macro
 @butensor
 ```
 
-When using the `CuTENSORBackend()` and no allocator is specified, it will automatically select the
+When using the `cuTENSORBackend()` and no allocator is specified, it will automatically select the
 allocator `CUDAAllocator()`, which will create new temporaries as `CuArray` objects. However,
 `CUDAAllocator` has three type parameters which can be used to customize the behavior of the allocator
 with respect to temporaries, as well as input and output tensors.
@@ -165,4 +165,4 @@ TensorOperations.CUDAAllocator
 
 Users can also define their own allocators, to facilitate experimentation with new implementations.
 Here, no restriction is made on the type of the allocator, and any object can be passed as an allocator.
-The required implementated methods are [`tensoralloc`](@ref) and [`tensorfree!`](@ref).
+The required implemented methods are [`tensoralloc`](@ref) and [`tensorfree!`](@ref).

docs/src/man/indexnotation.md

@@ -362,7 +362,7 @@ TensorOperations.IndexError
 ```
 
 Once the expression is compiled, there can still be errors that will lead to runtime errors,
-the type of which depends ont he specific type of tensor (e.g. `DimensionMismatch` for
+the type of which depends on the specific type of tensor (e.g. `DimensionMismatch` for
 `AbstractArray` objects). Indeed, indices with the same label, either open indices on the 
 two sides of the equation, or contracted indices, need to be compatible. For `AbstractArray` 
 objects, this means they must have the same size. Other tensor types might have more complicated 
@@ -384,11 +384,11 @@ TensorOperations.dimcheck_tensorcontract
 ```
 
 Whenever an incompatible index structures is detected at runtime, the resulting error will
-originate deep within the implementation,  at which point the error message will provide 
-little information as to which specific tensors  and which indices are producing the mismatch. 
-When debugging, it might be useful to add the  keyword argument `contractcheck = true` to 
-the `@tensor` macro. Explicit checks using  `checkcontractible` are then enabled that are run 
-before any tensor operation is performed.  When a mismatch is detected, these checks still 
+originate deep within the implementation, at which point the error message will provide 
+little information as to which specific tensors and which indices are producing the mismatch. 
+When debugging, it might be useful to add the keyword argument `contractcheck = true` to 
+the `@tensor` macro. Explicit checks using `checkcontractible` are then enabled that are run 
+before any tensor operation is performed. When a mismatch is detected, these checks still 
 have access to the label information and spawn a more informative error message.
 
 A different type of check is the `costcheck` keyword argument, which can be given the values
@@ -454,4 +454,4 @@ operations.
 
 ```@docs
 @cutensor
-```
+```