diff --git a/stdlib/LinearAlgebra/src/bidiag.jl b/stdlib/LinearAlgebra/src/bidiag.jl
index 0caaec02b5056..24958422015ab 100644
--- a/stdlib/LinearAlgebra/src/bidiag.jl
+++ b/stdlib/LinearAlgebra/src/bidiag.jl
@@ -305,7 +305,7 @@ function _copyto_banded!(A::Bidiagonal, B::Bidiagonal)
     if A.uplo == B.uplo
         A.ev .= B.ev
     elseif iszero(B.ev) # diagonal source
-        A.ev .= zero.(A.ev)
+        A.ev .= B.ev
     else
         zeroband = istriu(A) ? "lower" : "upper"
         uplo = A.uplo
diff --git a/stdlib/LinearAlgebra/src/special.jl b/stdlib/LinearAlgebra/src/special.jl
index 9633594574055..28a1b4b1b2eab 100644
--- a/stdlib/LinearAlgebra/src/special.jl
+++ b/stdlib/LinearAlgebra/src/special.jl
@@ -320,20 +320,20 @@ function copyto!(dest::BandedMatrix, src::BandedMatrix)
 end
 function _copyto_banded!(T::Tridiagonal, D::Diagonal)
     T.d .= D.diag
-    T.dl .= zero.(T.dl)
-    T.du .= zero.(T.du)
+    T.dl .= view(D, diagind(D, -1, IndexStyle(D)))
+    T.du .= view(D, diagind(D,  1, IndexStyle(D)))
     return T
 end
 function _copyto_banded!(SymT::SymTridiagonal, D::Diagonal)
     issymmetric(D) || throw(ArgumentError("cannot copy a non-symmetric Diagonal matrix to a SymTridiagonal"))
     SymT.dv .= D.diag
     _ev = _evview(SymT)
-    _ev .= zero.(_ev)
+    _ev .= view(D, diagind(D,  1, IndexStyle(D)))
     return SymT
 end
 function _copyto_banded!(B::Bidiagonal, D::Diagonal)
     B.dv .= D.diag
-    B.ev .= zero.(B.ev)
+    B.ev .= view(D, diagind(D,  B.uplo == 'U' ? 1 : -1, IndexStyle(D)))
     return B
 end
 function _copyto_banded!(D::Diagonal, B::Bidiagonal)
@@ -361,10 +361,10 @@ function _copyto_banded!(T::Tridiagonal, B::Bidiagonal)
     T.d .= B.dv
     if B.uplo == 'U'
         T.du .= B.ev
-        T.dl .= zero.(T.dl)
+        T.dl .= view(B, diagind(B, -1, IndexStyle(B)))
     else
         T.dl .= B.ev
-        T.du .= zero.(T.du)
+        T.du .= view(B, diagind(B,  1, IndexStyle(B)))
     end
     return T
 end
@@ -372,7 +372,7 @@ function _copyto_banded!(SymT::SymTridiagonal, B::Bidiagonal)
     issymmetric(B) || throw(ArgumentError("cannot copy a non-symmetric Bidiagonal matrix to a SymTridiagonal"))
     SymT.dv .= B.dv
     _ev = _evview(SymT)
-    _ev .= zero.(_ev)
+    _ev .= B.ev
     return SymT
 end
 function _copyto_banded!(B::Bidiagonal, T::Tridiagonal)
diff --git a/stdlib/LinearAlgebra/src/tridiag.jl b/stdlib/LinearAlgebra/src/tridiag.jl
index 2ff688f4b4ed1..e217425402df9 100644
--- a/stdlib/LinearAlgebra/src/tridiag.jl
+++ b/stdlib/LinearAlgebra/src/tridiag.jl
@@ -1040,7 +1040,7 @@ function _copyto_banded!(A::Tridiagonal, B::SymTridiagonal)
     return A
 end
 function _copyto_banded!(A::SymTridiagonal, B::Tridiagonal)
-    issymmetric(B) || throw(ArgumentError("cannot copy a non-symmetric Tridiagonal matrix to a SymTridiagonal"))
+    issymmetric(B) || throw(ArgumentError("cannot copy an asymmetric Tridiagonal matrix to a SymTridiagonal"))
     A.dv .= B.d
     _evview(A) .= B.du
     return A
diff --git a/stdlib/LinearAlgebra/test/special.jl b/stdlib/LinearAlgebra/test/special.jl
index 2f870373c9586..9bb84ba0e9d03 100644
--- a/stdlib/LinearAlgebra/test/special.jl
+++ b/stdlib/LinearAlgebra/test/special.jl
@@ -555,8 +555,8 @@ end
     @testset "from Diagonal" begin
         D = Diagonal(d)
         @testset "to Bidiagonal" begin
-            BU = Bidiagonal(zero(d), oneunit.(du), :U)
-            BL = Bidiagonal(zero(d), oneunit.(dl), :L)
+            BU = Bidiagonal(similar(d, BigInt), similar(du, BigInt), :U)
+            BL = Bidiagonal(similar(d, BigInt), similar(dl, BigInt), :L)
             for B in (BL, BU)
                 copyto!(B, D)
                 @test B == D
@@ -573,7 +573,7 @@ end
             end
         end
         @testset "to Tridiagonal" begin
-            T = Tridiagonal(oneunit.(dl), zero(d), oneunit.(du))
+            T = Tridiagonal(similar(dl, BigInt), similar(d, BigInt), similar(du, BigInt))
             copyto!(T, D)
             @test T == D
 
@@ -586,8 +586,8 @@ end
             end
         end
         @testset "to SymTridiagonal" begin
-            for du2 in (oneunit.(du), oneunit.(d))
-                S = SymTridiagonal(zero(d), du2)
+            for du2 in (similar(du, BigInt), similar(d, BigInt))
+                S = SymTridiagonal(similar(d), du2)
                 copyto!(S, D)
                 @test S == D
             end
@@ -630,13 +630,14 @@ end
             end
         end
         @testset "to Tridiagonal" begin
-            T = Tridiagonal(oneunit.(dl), zero(d), oneunit.(du))
+            T = Tridiagonal(similar(dl, BigInt), similar(d, BigInt), similar(du, BigInt))
             for B in (BL, BU, BLones, BUones)
                 copyto!(T, B)
                 @test T == B
             end
 
             @testset "mismatched size" begin
+                T = Tridiagonal(oneunit.(dl), zero(d), oneunit.(du))
                 for uplo in (:L, :U)
                     T .= 0
                     copyto!(T, Bidiagonal([1], Int[], uplo))
@@ -647,8 +648,8 @@ end
             end
         end
         @testset "to SymTridiagonal" begin
-            for du2 in (oneunit.(du), oneunit.(d))
-                S = SymTridiagonal(zero(d), du2)
+            for du2 in (similar(du, BigInt), similar(d, BigInt))
+                S = SymTridiagonal(similar(d, BigInt), du2)
                 for B in (BL, BU)
                     copyto!(S, B)
                     @test S == B
diff --git a/stdlib/LinearAlgebra/test/tridiag.jl b/stdlib/LinearAlgebra/test/tridiag.jl
index 5dc1d01e850d8..41a28631b27a0 100644
--- a/stdlib/LinearAlgebra/test/tridiag.jl
+++ b/stdlib/LinearAlgebra/test/tridiag.jl
@@ -808,7 +808,7 @@ end
     @test copyto!(zero(S), T) == T
 
     T2 = Tridiagonal(ones(length(ev)), zero(dv), zero(ev))
-    @test_throws "cannot copy a non-symmetric Tridiagonal matrix to a SymTridiagonal" copyto!(zero(S), T2)
+    @test_throws "cannot copy an asymmetric Tridiagonal matrix to a SymTridiagonal" copyto!(zero(S), T2)
 
     @testset "mismatched sizes" begin
         dv2 = [4; @view dv[2:end]]