document Upper/LowerTriangular

and clarify that Symmetric/Hermitian are views as well

add references to Upper/LowerTriangular in the manual

base/linalg/cholesky.jl

@@ -162,7 +162,7 @@ end
  chol(A) -> U
 
 Compute the Cholesky factorization of a positive definite matrix `A`
-and return the UpperTriangular matrix `U` such that `A = U'U`.
+and return the [`UpperTriangular`](@ref) matrix `U` such that `A = U'U`.
 
 # Example
 

base/linalg/symmetric.jl

@@ -8,7 +8,8 @@ end
 """
  Symmetric(A, uplo=:U)
 
-Construct a `Symmetric` matrix from the upper (if `uplo = :U`) or lower (if `uplo = :L`) triangle of `A`.
+Construct a `Symmetric` view of the upper (if `uplo = :U`) or lower (if `uplo = :L`)
+triangle of the matrix `A`.
 
 # Example
 
@@ -49,7 +50,8 @@ end
 """
  Hermitian(A, uplo=:U)
 
-Construct a `Hermitian` matrix from the upper (if `uplo = :U`) or lower (if `uplo = :L`) triangle of `A`.
+Construct a `Hermitian` view of the upper (if `uplo = :U`) or lower (if `uplo = :L`)
+triangle of the matrix `A`.
 
 # Example
 

base/linalg/triangular.jl

@@ -50,6 +50,51 @@ LowerTriangular(U::UpperTriangular) = throw(ArgumentError(
 UpperTriangular(U::LowerTriangular) = throw(ArgumentError(
  "cannot create an UpperTriangular matrix from a LowerTriangular input"))
 
+"""
+ LowerTriangular(A::AbstractMatrix)
+
+Construct a `LowerTriangular` view of the the matrix `A`.
+
+# Example
+
+```jldoctest
+julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]
+3×3 Array{Float64,2}:
+ 1.0 2.0 3.0
+ 4.0 5.0 6.0
+ 7.0 8.0 9.0
+
+julia> LowerTriangular(A)
+3×3 LowerTriangular{Float64,Array{Float64,2}}:
+ 1.0 ⋅ ⋅
+ 4.0 5.0 ⋅
+ 7.0 8.0 9.0
+```
+"""
+LowerTriangular
+"""
+ UpperTriangular(A::AbstractMatrix)
+
+Construct an `UpperTriangular` view of the the matrix `A`.
+
+# Example
+
+```jldoctest
+julia> A = [1.0 2.0 3.0; 4.0 5.0 6.0; 7.0 8.0 9.0]
+3×3 Array{Float64,2}:
+ 1.0 2.0 3.0
+ 4.0 5.0 6.0
+ 7.0 8.0 9.0
+
+julia> UpperTriangular(A)
+3×3 UpperTriangular{Float64,Array{Float64,2}}:
+ 1.0 2.0 3.0
+ ⋅ 5.0 6.0
+ ⋅ ⋅ 9.0
+```
+"""
+UpperTriangular
+
 imag(A::UpperTriangular) = UpperTriangular(imag(A.data))
 imag(A::LowerTriangular) = LowerTriangular(imag(A.data))
 imag(A::UnitLowerTriangular) = LowerTriangular(tril!(imag(A.data),-1))

doc/src/manual/linear-algebra.md

@@ -144,29 +144,29 @@ specialized routines that are specially developed for particular matrix types.
 The following tables summarize the types of special matrices that have been implemented in Julia,
 as well as whether hooks to various optimized methods for them in LAPACK are available.
 
-| Type | Description |
-|:------------------------ |:-------------------------------------------------------------------------------- |
-| [`Hermitian`](@ref) | [Hermitian matrix](https://en.wikipedia.org/wiki/Hermitian_matrix) |
-| `UpperTriangular`  | Upper [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) |
-| `LowerTriangular`  | Lower [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) |
-| [`Tridiagonal`](@ref) | [Tridiagonal matrix](https://en.wikipedia.org/wiki/Tridiagonal_matrix) |
-| [`SymTridiagonal`](@ref) | Symmetric tridiagonal matrix |
-| [`Bidiagonal`](@ref) | Upper/lower [bidiagonal matrix](https://en.wikipedia.org/wiki/Bidiagonal_matrix) |
-| [`Diagonal`](@ref) | [Diagonal matrix](https://en.wikipedia.org/wiki/Diagonal_matrix) |
-| `UniformScaling` | [Uniform scaling operator](https://en.wikipedia.org/wiki/Uniform_scaling) |
+| Type  | Description |
+|:------------------------- |:-------------------------------------------------------------------------------- |
+| [`Hermitian`](@ref)  | [Hermitian matrix](https://en.wikipedia.org/wiki/Hermitian_matrix) |
+| [`UpperTriangular`](@ref) | Upper [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) |
+| [`LowerTriangular`](@ref) | Lower [triangular matrix](https://en.wikipedia.org/wiki/Triangular_matrix) |
+| [`Tridiagonal`](@ref)  | [Tridiagonal matrix](https://en.wikipedia.org/wiki/Tridiagonal_matrix) |
+| [`SymTridiagonal`](@ref)  | Symmetric tridiagonal matrix |
+| [`Bidiagonal`](@ref)  | Upper/lower [bidiagonal matrix](https://en.wikipedia.org/wiki/Bidiagonal_matrix) |
+| [`Diagonal`](@ref)  | [Diagonal matrix](https://en.wikipedia.org/wiki/Diagonal_matrix) |
+| `UniformScaling`  | [Uniform scaling operator](https://en.wikipedia.org/wiki/Uniform_scaling) |
 
 ### Elementary operations
 
-| Matrix type | `+` | `-` | `*` | `\` | Other functions with optimized methods |
-|:------------------------ |:--- |:--- |:--- |:--- |:------------------------------------------------------------------- |
-| [`Hermitian`](@ref) |   |   |   | MV | [`inv()`](@ref), [`sqrtm()`](@ref), [`expm()`](@ref) |
-| `UpperTriangular`  |   |   | MV | MV | [`inv()`](@ref), [`det()`](@ref) |
-| `LowerTriangular`  |   |   | MV | MV | [`inv()`](@ref), [`det()`](@ref) |
-| [`SymTridiagonal`](@ref) | M | M | MS | MV | [`eigmax()`](@ref), [`eigmin()`](@ref) |
-| [`Tridiagonal`](@ref) | M | M | MS | MV |   |
-| [`Bidiagonal`](@ref) | M | M | MS | MV |   |
-| [`Diagonal`](@ref) | M | M | MV | MV | [`inv()`](@ref), [`det()`](@ref), [`logdet()`](@ref), [`/()`](@ref) |
-| `UniformScaling` | M | M | MVS | MVS | [`/()`](@ref) |
+| Matrix type  | `+` | `-` | `*` | `\` | Other functions with optimized methods |
+|:------------------------- |:--- |:--- |:--- |:--- |:------------------------------------------------------------------- |
+| [`Hermitian`](@ref)  |   |   |   | MV | [`inv()`](@ref), [`sqrtm()`](@ref), [`expm()`](@ref) |
+| [`UpperTriangular`](@ref) |   |   | MV | MV | [`inv()`](@ref), [`det()`](@ref) |
+| [`LowerTriangular`](@ref) |   |   | MV | MV | [`inv()`](@ref), [`det()`](@ref) |
+| [`SymTridiagonal`](@ref)  | M | M | MS | MV | [`eigmax()`](@ref), [`eigmin()`](@ref) |
+| [`Tridiagonal`](@ref)  | M | M | MS | MV |   |
+| [`Bidiagonal`](@ref)  | M | M | MS | MV |   |
+| [`Diagonal`](@ref)  | M | M | MV | MV | [`inv()`](@ref), [`det()`](@ref), [`logdet()`](@ref), [`/()`](@ref) |
+| `UniformScaling`  | M | M | MVS | MVS | [`/()`](@ref) |
 
 Legend:
 
@@ -178,15 +178,15 @@ Legend:
 
 ### Matrix factorizations
 
-| Matrix type | LAPACK | [`eig()`](@ref) | [`eigvals()`](@ref) | [`eigvecs()`](@ref) | [`svd()`](@ref) | [`svdvals()`](@ref) |
-|:------------------------ |:------ |:--------------- |:------------------- |:------------------- |:--------------- |:------------------- |
-| [`Hermitian`](@ref) | HE |   | ARI |   |   |   |
-| `UpperTriangular`  | TR | A | A | A |   |   |
-| `LowerTriangular`  | TR | A | A | A |   |   |
-| [`SymTridiagonal`](@ref) | ST | A | ARI | AV |   |   |
-| [`Tridiagonal`](@ref) | GT |   |   |   |   |   |
-| [`Bidiagonal`](@ref) | BD |   |   |   | A | A |
-| [`Diagonal`](@ref) | DI |   | A |   |   |   |
+| Matrix type  | LAPACK | [`eig()`](@ref) | [`eigvals()`](@ref) | [`eigvecs()`](@ref) | [`svd()`](@ref) | [`svdvals()`](@ref) |
+|:------------------------- |:------ |:--------------- |:------------------- |:------------------- |:--------------- |:------------------- |
+| [`Hermitian`](@ref)  | HE |   | ARI |   |   |   |
+| [`UpperTriangular`](@ref) | TR | A | A | A |   |   |
+| [`LowerTriangular`](@ref) | TR | A | A | A |   |   |
+| [`SymTridiagonal`](@ref)  | ST | A | ARI | AV |   |   |
+| [`Tridiagonal`](@ref)  | GT |   |   |   |   |   |
+| [`Bidiagonal`](@ref)  | BD |   |   |   | A | A |
+| [`Diagonal`](@ref)  | DI |   | A |   |   |   |
 
 Legend:
 

doc/src/stdlib/linalg.md

@@ -18,6 +18,8 @@ Base.LinAlg.SymTridiagonal
 Base.LinAlg.Tridiagonal
 Base.LinAlg.Symmetric
 Base.LinAlg.Hermitian
+Base.LinAlg.LowerTriangular
+Base.LinAlg.UpperTriangular
 Base.LinAlg.lu
 Base.LinAlg.lufact
 Base.LinAlg.lufact!