Avoid out of bounds read in mul! for SymTridiagonal (#27008)

* Avoid out of bounds read in mul! for SymTridiagonal

Fixes #26994

* Also handle 0x0 case

stdlib/LinearAlgebra/src/tridiag.jl

@@ -157,14 +157,19 @@ function mul!(C::StridedVecOrMat, S::SymTridiagonal, B::StridedVecOrMat)
         throw(DimensionMismatch("second dimension of B, $n, doesn't match second dimension of C, $(size(C,2))"))
     end
 
+    if m == 0
+        return C
+    end
+
     α = S.dv
     β = S.ev
     @inbounds begin
         for j = 1:n
-            x₀, x₊ = B[1, j], B[2, j]
-            β₀ = β[1]
-            C[1, j] = α[1]*x₀ + x₊*β₀
-            for i = 2:m - 1
+            x₊ = B[1, j]
+            x₀ = zero(x₊)
+            # If m == 1 then β[1] is out of bounds
+            β₀ = m > 1 ? zero(β[1]) : zero(eltype(β))
+            for i = 1:m - 1
                 x₋, x₀, x₊ = x₀, x₊, B[i + 1, j]
                 β₋, β₀ = β₀, β[i]
                 C[i, j] = β₋*x₋ + α[i]*x₀ + β₀*x₊

stdlib/LinearAlgebra/test/tridiag.jl

@@ -353,4 +353,11 @@ end
     @test Tridiagonal(4:5, 1:3, 1:2) == [1 1 0; 4 2 2; 0 5 3]
 end
 
+@testset "Issue #26994 (and the empty case)" begin
+    T = SymTridiagonal([1.0],[3.0])
+    x = ones(1)
+    @test T*x == ones(1)
+    @test SymTridiagonal(ones(0), ones(0)) * ones(0, 2) == ones(0, 2)
+end
+
 end # module TestTridiagonal