apply suggestions

Author: lkdvos

docs/src/user_interface/decompositions.md

@@ -270,7 +270,7 @@ true
 ## Null Spaces
 
 Similarly, it can be convenient to obtain an orthogonal basis for the kernel or cokernel of a matrix.
-These are the complements of the coimage and image, respectively, and can be computed using the [`left_null`](@ref) and [`right_null`](@ref) functions.
+These are the orthogonal complements of the coimage and image, respectively, and can be computed using the [`left_null`](@ref) and [`right_null`](@ref) functions.
 
 ### Overview
 

src/algorithms.jl

@@ -55,7 +55,6 @@ end
 
 # Algorithm traits
 # ----------------
-
 """
     does_truncate(alg::AbstractAlgorithm) -> Bool
 

src/implementations/orthnull.jl

@@ -7,7 +7,6 @@ copy_input(::typeof(right_null), A) = copy_input(lq_null, A) # do we ever need a
 
 check_input(::typeof(left_orth!), A, VC, alg::AbstractAlgorithm) =
     check_input(left_orth!, A, VC, left_orth_alg(alg))
-
 check_input(::typeof(left_orth!), A, VC, alg::LeftOrthViaQR) =
     check_input(qr_compact!, A, VC, alg.alg)
 check_input(::typeof(left_orth!), A, VC, alg::LeftOrthViaPolar) =
@@ -16,7 +15,6 @@ check_input(::typeof(left_orth!), A, VC, alg::LeftOrthViaSVD) = nothing
 
 check_input(::typeof(right_orth!), A, CVᴴ, alg::AbstractAlgorithm) =
     check_input(right_orth!, A, CVᴴ, right_orth_alg(alg))
-
 check_input(::typeof(right_orth!), A, VC, alg::RightOrthViaLQ) =
     check_input(lq_compact!, A, VC, alg.alg)
 check_input(::typeof(right_orth!), A, VC, alg::RightOrthViaPolar) =
@@ -39,7 +37,6 @@ check_input(::typeof(right_null!), A, Nᴴ, alg::RightNullViaSVD) = nothing
 # -------
 initialize_output(::typeof(left_orth!), A, alg::AbstractAlgorithm) =
     initialize_output(left_orth!, A, left_orth_alg(alg))
-
 initialize_output(::typeof(left_orth!), A, alg::LeftOrthViaQR) =
     initialize_output(qr_compact!, A, alg.alg)
 initialize_output(::typeof(left_orth!), A, alg::LeftOrthViaPolar) =
@@ -48,7 +45,6 @@ initialize_output(::typeof(left_orth!), A, alg::LeftOrthViaSVD) = nothing
 
 initialize_output(::typeof(right_orth!), A, alg::AbstractAlgorithm) =
     initialize_output(right_orth!, A, right_orth_alg(alg))
-
 initialize_output(::typeof(right_orth!), A, alg::RightOrthViaLQ) =
     initialize_output(lq_compact!, A, alg.alg)
 initialize_output(::typeof(right_orth!), A, alg::RightOrthViaPolar) =

src/interface/orthnull.jl

@@ -60,7 +60,7 @@ the chosen decomposition type. By default, the supported kinds are:
   and is roughly equivalent to:
 ```julia
         V, S, C = svd_trunc(A; trunc, kwargs...)
-        C = S * C
+        C = lmul!(S, C)
 ```
 
 ### `alg::AbstractAlgorithm`
@@ -141,7 +141,7 @@ the chosen decomposition type. By default, the supported kinds are:
   and is roughly equivalent to:
 ```julia
         C, S, Vᴴ = svd_trunc(A; trunc, kwargs...)
-        C = C * S
+        C = rmul!(C, S)
 ```
 
 ### `alg::AbstractAlgorithm`