diff --git a/NEWS.md b/NEWS.md
index c96d1a2365410..028c388d754aa 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -69,6 +69,8 @@ Standard library changes
   `Factorization` ([#46874]).
 * New functions `hermitianpart` and `hermitianpart!` for extracting the Hermitian
   (real symmetric) part of a matrix ([#31836]).
+* The `norm` of the adjoint or transpose of an `AbstractMatrix` now returns the norm of the
+  parent matrix by default, matching the current behaviour for `AbstractVector`s ([#49020]).
 
 #### Printf
 * Format specifiers now support dynamic width and precision, e.g. `%*s` and `%*.*g` ([#40105]).
diff --git a/stdlib/LinearAlgebra/src/generic.jl b/stdlib/LinearAlgebra/src/generic.jl
index ede42c2dbf9d7..0c947936dee6b 100644
--- a/stdlib/LinearAlgebra/src/generic.jl
+++ b/stdlib/LinearAlgebra/src/generic.jl
@@ -805,7 +805,7 @@ opnorm(v::AdjointAbsVec, q::Real) = q == Inf ? norm(conj(v.parent), 1) : norm(co
 opnorm(v::AdjointAbsVec) = norm(conj(v.parent))
 opnorm(v::TransposeAbsVec) = norm(v.parent)
 
-norm(v::Union{TransposeAbsVec,AdjointAbsVec}, p::Real) = norm(v.parent, p)
+norm(v::AdjOrTrans, p::Real) = norm(v.parent, p)
 
 """
     dot(x, y)
diff --git a/stdlib/LinearAlgebra/test/generic.jl b/stdlib/LinearAlgebra/test/generic.jl
index a95827867cd18..108d3aec8f069 100644
--- a/stdlib/LinearAlgebra/test/generic.jl
+++ b/stdlib/LinearAlgebra/test/generic.jl
@@ -269,6 +269,24 @@ end
     @test norm(x, 3) ≈ cbrt(5^3  +sqrt(5)^3)
 end
 
+@testset "norm of transpose/adjoint equals norm of parent #32739" begin
+    for t in (transpose, adjoint), elt in (Float32, Float64, BigFloat, ComplexF32, ComplexF64, Complex{BigFloat})
+        # Vector/matrix of scalars
+        for sz in ((2,), (2, 3))
+            A = rand(elt, sz...)
+            Aᵀ = t(A)
+            @test norm(Aᵀ) ≈ norm(Matrix(Aᵀ))
+        end
+
+        # Vector/matrix of vectors/matrices
+        for sz_outer in ((2,), (2, 3)), sz_inner in ((3,), (1, 2))
+            A = [rand(elt, sz_inner...) for _ in CartesianIndices(sz_outer)]
+            Aᵀ = t(A)
+            @test norm(Aᵀ) ≈ norm(Matrix(Matrix.(Aᵀ)))
+        end
+    end
+end
+
 @testset "rotate! and reflect!" begin
     x = rand(ComplexF64, 10)
     y = rand(ComplexF64, 10)