Implement isdiag(::Bidiagonal), add tests (#32694)

Author: garrison

stdlib/LinearAlgebra/src/bidiag.jl

@@ -250,6 +250,7 @@ iszero(M::Bidiagonal) = iszero(M.dv) && iszero(M.ev)
 isone(M::Bidiagonal) = all(isone, M.dv) && iszero(M.ev)
 istriu(M::Bidiagonal) = M.uplo == 'U' || iszero(M.ev)
 istril(M::Bidiagonal) = M.uplo == 'L' || iszero(M.ev)
+isdiag(M::Bidiagonal) = iszero(M.ev)
 
 function tril!(M::Bidiagonal, k::Integer=0)
     n = length(M.dv)

stdlib/LinearAlgebra/test/bidiag.jl

@@ -156,6 +156,10 @@ Random.seed!(1)
             @test triu!(bidiagcopy(dv,ev,:U))    == Bidiagonal(dv,ev,:U)
             @test_throws ArgumentError triu!(bidiagcopy(dv, ev, :U), -n)
             @test_throws ArgumentError triu!(bidiagcopy(dv, ev, :U), n + 2)
+            @test !isdiag(Bidiagonal(dv,ev,:U))
+            @test !isdiag(Bidiagonal(dv,ev,:L))
+            @test isdiag(Bidiagonal(dv,zerosev,:U))
+            @test isdiag(Bidiagonal(dv,zerosev,:L))
         end
 
         @testset "iszero and isone" begin