diff --git a/stdlib/LinearAlgebra/src/generic.jl b/stdlib/LinearAlgebra/src/generic.jl
index a93325ed5b883..df4112134bc81 100644
--- a/stdlib/LinearAlgebra/src/generic.jl
+++ b/stdlib/LinearAlgebra/src/generic.jl
@@ -2014,19 +2014,24 @@ function copytrito!(B::AbstractMatrix, A::AbstractMatrix, uplo::AbstractChar)
     BLAS.chkuplo(uplo)
     m,n = size(A)
     m1,n1 = size(B)
-    (m1 < m || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least the same number of rows and columns than A of size ($m,$n)"))
     A = Base.unalias(B, A)
     if uplo == 'U'
-        for j=1:n
-            for i=1:min(j,m)
-                @inbounds B[i,j] = A[i,j]
-            end
+        if n < m
+            (m1 < n || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($n,$n)"))
+        else
+            (m1 < m || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($m,$n)"))
         end
-    else  # uplo == 'L'
-        for j=1:n
-            for i=j:m
-                @inbounds B[i,j] = A[i,j]
-            end
+        for j in 1:n, i in 1:min(j,m)
+            @inbounds B[i,j] = A[i,j]
+        end
+    else # uplo == 'L'
+        if m < n
+            (m1 < m || n1 < m) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($m,$m)"))
+        else
+            (m1 < m || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($m,$n)"))
+        end
+        for j in 1:n, i in j:m
+            @inbounds B[i,j] = A[i,j]
         end
     end
     return B
diff --git a/stdlib/LinearAlgebra/src/lapack.jl b/stdlib/LinearAlgebra/src/lapack.jl
index b7c624dbb494d..c9f018e21175a 100644
--- a/stdlib/LinearAlgebra/src/lapack.jl
+++ b/stdlib/LinearAlgebra/src/lapack.jl
@@ -7157,9 +7157,23 @@ for (fn, elty) in ((:dlacpy_, :Float64),
         function lacpy!(B::AbstractMatrix{$elty}, A::AbstractMatrix{$elty}, uplo::AbstractChar)
             require_one_based_indexing(A, B)
             chkstride1(A, B)
-            m,n = size(A)
-            m1,n1 = size(B)
-            (m1 < m || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least the same number of rows and columns than A of size ($m,$n)"))
+            m, n = size(A)
+            m1, n1 = size(B)
+            if uplo == 'U'
+                if n < m
+                    (m1 < n || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($n,$n)"))
+                else
+                    (m1 < m || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($m,$n)"))
+                end
+            elseif uplo == 'L'
+                if m < n
+                    (m1 < m || n1 < m) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($m,$m)"))
+                else
+                    (m1 < m || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($m,$n)"))
+                end
+            else
+                (m1 < m || n1 < n) && throw(DimensionMismatch(lazy"B of size ($m1,$n1) should have at least size ($m,$n)"))
+            end
             lda = max(1, stride(A, 2))
             ldb = max(1, stride(B, 2))
             ccall((@blasfunc($fn), libblastrampoline), Cvoid,
diff --git a/stdlib/LinearAlgebra/test/generic.jl b/stdlib/LinearAlgebra/test/generic.jl
index f4eff3b2e355f..e0a1704913f78 100644
--- a/stdlib/LinearAlgebra/test/generic.jl
+++ b/stdlib/LinearAlgebra/test/generic.jl
@@ -654,12 +654,54 @@ end
 
 @testset "copytrito!" begin
     n = 10
-    for A in (rand(n, n), rand(Int8, n, n)), uplo in ('L', 'U')
-        for AA in (A, view(A, reverse.(axes(A))...))
-            for B in (zeros(n, n), zeros(n+1, n+2))
-                copytrito!(B, AA, uplo)
+    @testset "square" begin
+        for A in (rand(n, n), rand(Int8, n, n)), uplo in ('L', 'U')
+            for AA in (A, view(A, reverse.(axes(A))...))
                 C = uplo == 'L' ? tril(AA) : triu(AA)
-                @test view(B, 1:n, 1:n) == C
+                for B in (zeros(n, n), zeros(n+1, n+2))
+                    copytrito!(B, AA, uplo)
+                    @test view(B, 1:n, 1:n) == C
+                end
+            end
+        end
+    end
+    @testset "wide" begin
+        for A in (rand(n, 2n), rand(Int8, n, 2n))
+            for AA in (A, view(A, reverse.(axes(A))...))
+                C = tril(AA)
+                for (M, N) in ((n, n), (n+1, n), (n, n+1), (n+1, n+1))
+                    B = zeros(M, N)
+                    copytrito!(B, AA, 'L')
+                    @test view(B, 1:n, 1:n) == view(C, 1:n, 1:n)
+                end
+                @test_throws DimensionMismatch copytrito!(zeros(n-1, 2n), AA, 'L')
+                C = triu(AA)
+                for (M, N) in ((n, 2n), (n+1, 2n), (n, 2n+1), (n+1, 2n+1))
+                    B = zeros(M, N)
+                    copytrito!(B, AA, 'U')
+                    @test view(B, 1:n, 1:2n) == view(C, 1:n, 1:2n)
+                end
+                @test_throws DimensionMismatch copytrito!(zeros(n+1, 2n-1), AA, 'U')
+            end
+        end
+    end
+    @testset "tall" begin
+        for A in (rand(2n, n), rand(Int8, 2n, n))
+            for AA in (A, view(A, reverse.(axes(A))...))
+                C = triu(AA)
+                for (M, N) in ((n, n), (n+1, n), (n, n+1), (n+1, n+1))
+                    B = zeros(M, N)
+                    copytrito!(B, AA, 'U')
+                    @test view(B, 1:n, 1:n) == view(C, 1:n, 1:n)
+                end
+                @test_throws DimensionMismatch copytrito!(zeros(n-1, n+1), AA, 'U')
+                C = tril(AA)
+                for (M, N) in ((2n, n), (2n, n+1), (2n+1, n), (2n+1, n+1))
+                    B = zeros(M, N)
+                    copytrito!(B, AA, 'L')
+                    @test view(B, 1:2n, 1:n) == view(C, 1:2n, 1:n)
+                end
+                @test_throws DimensionMismatch copytrito!(zeros(n-1, n+1), AA, 'L')
             end
         end
     end
diff --git a/stdlib/LinearAlgebra/test/lapack.jl b/stdlib/LinearAlgebra/test/lapack.jl
index fe0dd92d0a69a..fd14dad4634a8 100644
--- a/stdlib/LinearAlgebra/test/lapack.jl
+++ b/stdlib/LinearAlgebra/test/lapack.jl
@@ -805,8 +805,26 @@ end
             B = zeros(elty, n, n)
             LinearAlgebra.LAPACK.lacpy!(B, A, uplo)
             C = uplo == 'L' ? tril(A) : (uplo == 'U' ? triu(A) : A)
-            @test B ≈ C
+            @test B == C
+            B = zeros(elty, n+1, n+1)
+            LinearAlgebra.LAPACK.lacpy!(B, A, uplo)
+            C = uplo == 'L' ? tril(A) : (uplo == 'U' ? triu(A) : A)
+            @test view(B, 1:n, 1:n) == C
         end
+        A = rand(elty, n, n+1)
+        B = zeros(elty, n, n)
+        LinearAlgebra.LAPACK.lacpy!(B, A, 'L')
+        @test B == view(tril(A), 1:n, 1:n)
+        B = zeros(elty, n, n+1)
+        LinearAlgebra.LAPACK.lacpy!(B, A, 'U')
+        @test B == triu(A)
+        A = rand(elty, n+1, n)
+        B = zeros(elty, n, n)
+        LinearAlgebra.LAPACK.lacpy!(B, A, 'U')
+        @test B == view(triu(A), 1:n, 1:n)
+        B = zeros(elty, n+1, n)
+        LinearAlgebra.LAPACK.lacpy!(B, A, 'L')
+        @test B == tril(A)
     end
 end