diff --git a/stdlib/SparseArrays/src/linalg.jl b/stdlib/SparseArrays/src/linalg.jl
index 25ddb3222f6b2..1ed2c680059ce 100644
--- a/stdlib/SparseArrays/src/linalg.jl
+++ b/stdlib/SparseArrays/src/linalg.jl
@@ -4,8 +4,10 @@ import LinearAlgebra: checksquare, sym_uplo
 using Random: rand!
 
 # In matrix-vector multiplication, the correct orientation of the vector is assumed.
-const StridedOrTriangularMatrix{T} = Union{StridedMatrix{T}, LowerTriangular{T}, UnitLowerTriangular{T}, UpperTriangular{T}, UnitUpperTriangular{T}}
-const AdjOrTransStridedOrTriangularMatrix{T} = Union{StridedOrTriangularMatrix{T},Adjoint{<:Any,<:StridedOrTriangularMatrix{T}},Transpose{<:Any,<:StridedOrTriangularMatrix{T}}}
+const DenseMatrixUnion = Union{StridedMatrix, LowerTriangular, UnitLowerTriangular, UpperTriangular, UnitUpperTriangular, BitMatrix}
+const AdjOrTransDenseMatrix = Union{DenseMatrixUnion,Adjoint{<:Any,<:DenseMatrixUnion},Transpose{<:Any,<:DenseMatrixUnion}}
+const DenseInputVector = Union{StridedVector, BitVector}
+const DenseInputVecOrMat = Union{AdjOrTransDenseMatrix, DenseInputVector}
 
 for op ∈ (:+, :-), Wrapper ∈ (:Hermitian, :Symmetric)
     @eval begin
@@ -25,7 +27,7 @@ for op ∈ (:+, :-)
     end
 end
 
-function mul!(C::StridedVecOrMat, A::AbstractSparseMatrixCSC, B::Union{StridedVector,AdjOrTransStridedOrTriangularMatrix}, α::Number, β::Number)
+function mul!(C::StridedVecOrMat, A::AbstractSparseMatrixCSC, B::DenseInputVecOrMat, α::Number, β::Number)
     size(A, 2) == size(B, 1) || throw(DimensionMismatch())
     size(A, 1) == size(C, 1) || throw(DimensionMismatch())
     size(B, 2) == size(C, 2) || throw(DimensionMismatch())
@@ -44,13 +46,14 @@ function mul!(C::StridedVecOrMat, A::AbstractSparseMatrixCSC, B::Union{StridedVe
     end
     C
 end
-*(A::SparseMatrixCSCUnion{TA}, x::StridedVector{Tx}) where {TA,Tx} =
-    (T = promote_op(matprod, TA, Tx); mul!(similar(x, T, size(A, 1)), A, x, true, false))
-*(A::SparseMatrixCSCUnion{TA}, B::AdjOrTransStridedOrTriangularMatrix{Tx}) where {TA,Tx} =
-    (T = promote_op(matprod, TA, Tx); mul!(similar(B, T, (size(A, 1), size(B, 2))), A, B, true, false))
+
+*(A::SparseMatrixCSCUnion{TA}, x::DenseInputVector) where {TA} =
+    (T = promote_op(matprod, TA, eltype(x)); mul!(similar(x, T, size(A, 1)), A, x, true, false))
+*(A::SparseMatrixCSCUnion{TA}, B::AdjOrTransDenseMatrix) where {TA} =
+    (T = promote_op(matprod, TA, eltype(B)); mul!(similar(B, T, (size(A, 1), size(B, 2))), A, B, true, false))
 
 for (T, t) in ((Adjoint, adjoint), (Transpose, transpose))
-    @eval function mul!(C::StridedVecOrMat, xA::$T{<:Any,<:AbstractSparseMatrixCSC}, B::Union{StridedVector,AdjOrTransStridedOrTriangularMatrix}, α::Number, β::Number)
+    @eval function mul!(C::StridedVecOrMat, xA::$T{<:Any,<:AbstractSparseMatrixCSC}, B::DenseInputVecOrMat, α::Number, β::Number)
         A = xA.parent
         size(A, 2) == size(C, 1) || throw(DimensionMismatch())
         size(A, 1) == size(B, 1) || throw(DimensionMismatch())
@@ -72,16 +75,16 @@ for (T, t) in ((Adjoint, adjoint), (Transpose, transpose))
         C
     end
 end
-*(adjA::Adjoint{<:Any,<:AbstractSparseMatrixCSC}, x::StridedVector{Tx}) where {Tx} =
-    (T = promote_op(matprod, eltype(adjA), Tx); mul!(similar(x, T, size(adjA, 1)), adjA, x, true, false))
-*(adjA::Adjoint{<:Any,<:AbstractSparseMatrixCSC}, B::AdjOrTransStridedOrTriangularMatrix) =
+*(adjA::Adjoint{<:Any,<:AbstractSparseMatrixCSC}, x::DenseInputVector) =
+    (T = promote_op(matprod, eltype(adjA), eltype(x)); mul!(similar(x, T, size(adjA, 1)), adjA, x, true, false))
+*(adjA::Adjoint{<:Any,<:AbstractSparseMatrixCSC}, B::AdjOrTransDenseMatrix) =
     (T = promote_op(matprod, eltype(adjA), eltype(B)); mul!(similar(B, T, (size(adjA, 1), size(B, 2))), adjA, B, true, false))
-*(transA::Transpose{<:Any,<:AbstractSparseMatrixCSC}, x::StridedVector{Tx}) where {Tx} =
-    (T = promote_op(matprod, eltype(transA), Tx); mul!(similar(x, T, size(transA, 1)), transA, x, true, false))
-*(transA::Transpose{<:Any,<:AbstractSparseMatrixCSC}, B::AdjOrTransStridedOrTriangularMatrix) =
+*(transA::Transpose{<:Any,<:AbstractSparseMatrixCSC}, x::DenseInputVector) =
+    (T = promote_op(matprod, eltype(transA), eltype(x)); mul!(similar(x, T, size(transA, 1)), transA, x, true, false))
+*(transA::Transpose{<:Any,<:AbstractSparseMatrixCSC}, B::AdjOrTransDenseMatrix) =
     (T = promote_op(matprod, eltype(transA), eltype(B)); mul!(similar(B, T, (size(transA, 1), size(B, 2))), transA, B, true, false))
 
-function mul!(C::StridedVecOrMat, X::AdjOrTransStridedOrTriangularMatrix, A::AbstractSparseMatrixCSC, α::Number, β::Number)
+function mul!(C::StridedVecOrMat, X::AdjOrTransDenseMatrix, A::AbstractSparseMatrixCSC, α::Number, β::Number)
     mX, nX = size(X)
     nX == size(A, 1) || throw(DimensionMismatch())
     mX == size(C, 1) || throw(DimensionMismatch())
@@ -91,7 +94,7 @@ function mul!(C::StridedVecOrMat, X::AdjOrTransStridedOrTriangularMatrix, A::Abs
     if β != 1
         β != 0 ? rmul!(C, β) : fill!(C, zero(eltype(C)))
     end
-    if X isa StridedOrTriangularMatrix
+    if X isa DenseMatrixUnion
         @inbounds for col in 1:size(A, 2), k in nzrange(A, col)
             Aiα = nzv[k] * α
             rvk = rv[k]
@@ -108,11 +111,11 @@ function mul!(C::StridedVecOrMat, X::AdjOrTransStridedOrTriangularMatrix, A::Abs
     end
     C
 end
-*(X::AdjOrTransStridedOrTriangularMatrix, A::SparseMatrixCSCUnion{TvA}) where {TvA} =
+*(X::AdjOrTransDenseMatrix, A::SparseMatrixCSCUnion{TvA}) where {TvA} =
     (T = promote_op(matprod, eltype(X), TvA); mul!(similar(X, T, (size(X, 1), size(A, 2))), X, A, true, false))
 
 for (T, t) in ((Adjoint, adjoint), (Transpose, transpose))
-    @eval function mul!(C::StridedVecOrMat, X::AdjOrTransStridedOrTriangularMatrix, xA::$T{<:Any,<:AbstractSparseMatrixCSC}, α::Number, β::Number)
+    @eval function mul!(C::StridedVecOrMat, X::AdjOrTransDenseMatrix, xA::$T{<:Any,<:AbstractSparseMatrixCSC}, α::Number, β::Number)
         A = xA.parent
         mX, nX = size(X)
         nX == size(A, 2) || throw(DimensionMismatch())
@@ -133,9 +136,9 @@ for (T, t) in ((Adjoint, adjoint), (Transpose, transpose))
         C
     end
 end
-*(X::AdjOrTransStridedOrTriangularMatrix, adjA::Adjoint{<:Any,<:AbstractSparseMatrixCSC}) =
+*(X::AdjOrTransDenseMatrix, adjA::Adjoint{<:Any,<:AbstractSparseMatrixCSC}) =
     (T = promote_op(matprod, eltype(X), eltype(adjA)); mul!(similar(X, T, (size(X, 1), size(adjA, 2))), X, adjA, true, false))
-*(X::AdjOrTransStridedOrTriangularMatrix, transA::Transpose{<:Any,<:AbstractSparseMatrixCSC}) =
+*(X::AdjOrTransDenseMatrix, transA::Transpose{<:Any,<:AbstractSparseMatrixCSC}) =
     (T = promote_op(matprod, eltype(X), eltype(transA)); mul!(similar(X, T, (size(X, 1), size(transA, 2))), X, transA, true, false))
 
 function (*)(D::Diagonal, A::AbstractSparseMatrixCSC)