diff --git a/src/dense.jl b/src/dense.jl
index 5fa28f85..25597369 100644
--- a/src/dense.jl
+++ b/src/dense.jl
@@ -237,22 +237,14 @@ end
 
 fillstored!(A::AbstractMatrix, v) = fill!(A, v)
 
-diagind(m::Integer, n::Integer, k::Integer=0) = diagind(IndexLinear(), m, n, k)
-diagind(::IndexLinear, m::Integer, n::Integer, k::Integer=0) =
-    k <= 0 ? range(1-k, step=m+1, length=min(m+k, n)) : range(k*m+1, step=m+1, length=min(m, n-k))
-
-function diagind(::IndexCartesian, m::Integer, n::Integer, k::Integer=0)
-    Cstart = CartesianIndex(1 + max(0,-k), 1 + max(0,k))
-    Cstep = CartesianIndex(1, 1)
-    length = max(0, k <= 0 ? min(m+k, n) : min(m, n-k))
-    StepRangeLen(Cstart, Cstep, length)
-end
-
 """
     diagind(M::AbstractMatrix, k::Integer = 0, indstyle::IndexStyle = IndexLinear())
     diagind(M::AbstractMatrix, indstyle::IndexStyle = IndexLinear())
+    diagind(::IndexStyle, m::Integer, n::Integer, k::Integer = 0)
+    diagind(m::Integer, n::Integer, k::Integer = 0)
 
-An `AbstractRange` giving the indices of the `k`th diagonal of the matrix `M`.
+An `AbstractRange` giving the indices of the `k`th diagonal of a matrix,
+specified either by the matrix `M` itself or by its dimensions `m` and `n`.
 Optionally, an index style may be specified which determines the type of the range returned.
 If `indstyle isa IndexLinear` (default), this returns an `AbstractRange{Integer}`.
 On the other hand, if `indstyle isa IndexCartesian`, this returns an `AbstractRange{CartesianIndex{2}}`.
@@ -262,6 +254,7 @@ If `k` is not provided, it is assumed to be `0` (corresponding to the main diago
 See also: [`diag`](@ref), [`diagm`](@ref), [`Diagonal`](@ref).
 
 # Examples
+The matrix itself may be passed to `diagind`:
 ```jldoctest
 julia> A = [1 2 3; 4 5 6; 7 8 9]
 3×3 Matrix{Int64}:
@@ -276,6 +269,18 @@ julia> diagind(A, IndexCartesian())
 StepRangeLen(CartesianIndex(1, 1), CartesianIndex(1, 1), 3)
 ```
 
+Alternatively, dimensions `m` and `n` may be passed to get the diagonal of an `m×n` matrix:
+```jldoctest
+julia> m, n = 5, 7
+(5, 7)
+
+julia> diagind(m, n, 2)
+11:6:35
+
+julia> diagind(IndexCartesian(), m, n)
+StepRangeLen(CartesianIndex(1, 1), CartesianIndex(1, 1), 5)
+```
+
 !!! compat "Julia 1.11"
      Specifying an `IndexStyle` requires at least Julia 1.11.
 """
@@ -286,6 +291,17 @@ end
 
 diagind(A::AbstractMatrix, indexstyle::IndexStyle) = diagind(A, 0, indexstyle)
 
+function diagind(::IndexCartesian, m::Integer, n::Integer, k::Integer=0)
+    Cstart = CartesianIndex(1 + max(0,-k), 1 + max(0,k))
+    Cstep = CartesianIndex(1, 1)
+    length = max(0, k <= 0 ? min(m+k, n) : min(m, n-k))
+    StepRangeLen(Cstart, Cstep, length)
+end
+
+diagind(::IndexLinear, m::Integer, n::Integer, k::Integer=0) =
+    k <= 0 ? range(1-k, step=m+1, length=min(m+k, n)) : range(k*m+1, step=m+1, length=min(m, n-k))
+diagind(m::Integer, n::Integer, k::Integer=0) = diagind(IndexLinear(), m, n, k)
+
 """
     diag(M, k::Integer=0)