diff --git a/src/common/matrixproperties.jl b/src/common/matrixproperties.jl
index 5a73176e..25876b90 100644
--- a/src/common/matrixproperties.jl
+++ b/src/common/matrixproperties.jl
@@ -157,7 +157,7 @@ function strided_ishermitian_approx(
     for j in 1:blocksize:n
         jb = min(blocksize, n - j + 1)
         ϵ² += _ishermitian_approx_diag(view(A, j:(j + jb - 1), j:(j + jb - 1)), anti)
-        ϵ² < ϵ²max || return false
+        ϵ² ≤ ϵ²max || return false
         for i in 1:blocksize:(j - 1)
             ib = blocksize
             ϵ² += 2 * _ishermitian_approx_offdiag(
@@ -165,7 +165,7 @@ function strided_ishermitian_approx(
                 view(A, j:(j + jb - 1), i:(i + ib - 1)),
                 anti
             )
-            ϵ² < ϵ²max || return false
+            ϵ² ≤ ϵ²max || return false
         end
     end
     return true
diff --git a/test/projections.jl b/test/projections.jl
index 3923528e..9a6644cf 100644
--- a/test/projections.jl
+++ b/test/projections.jl
@@ -1,4 +1,5 @@
 using MatrixAlgebraKit
+using MatrixAlgebraKit: check_hermitian, default_hermitian_tol
 using Test
 using TestExtras
 using StableRNGs
@@ -10,6 +11,12 @@ const BLASFloats = (Float32, Float64, ComplexF32, ComplexF64)
     rng = StableRNG(123)
     m = 54
     noisefactor = eps(real(T))^(3 / 4)
+
+    mat0 = zeros(T, (1, 1))
+    @test ishermitian(mat0)
+    @test ishermitian(mat0; atol = default_hermitian_tol(mat0))
+    @test isnothing(check_hermitian(mat0))
+
     for alg in (NativeBlocked(blocksize = 16), NativeBlocked(blocksize = 32), NativeBlocked(blocksize = 64))
         for A in (randn(rng, T, m, m), Diagonal(randn(rng, T, m)))
             Ah = (A + A') / 2