From 6ab3a5cfade50074adb0f3314236c9a84b7e2b8a Mon Sep 17 00:00:00 2001
From: Athan Reines <kgryte@gmail.com>
Date: Mon, 12 Apr 2021 11:02:56 -0700
Subject: [PATCH 1/2] Add specification for eigh

---
 .../linear_algebra_functions.md               | 33 +++++++++++++++++++
 1 file changed, 33 insertions(+)

diff --git a/spec/API_specification/linear_algebra_functions.md b/spec/API_specification/linear_algebra_functions.md
index 100efccf2..597ad0d76 100644
--- a/spec/API_specification/linear_algebra_functions.md
+++ b/spec/API_specification/linear_algebra_functions.md
@@ -107,6 +107,39 @@ TODO
 
 TODO
 
+(function-eigh)=
+### eigh(x, /, *, upper=False)
+
+Returns the eigenvalues and eigenvectors of a symmetric matrix (or a stack of symmetric matrices) `x`.
+
+<!-- NOTE: once complex number support, each matrix must be Hermitian -->
+
+#### Parameters
+
+-   **x**: _&lt;array&gt;_
+
+    -   input array having shape `(..., M, M)` and whose innermost two dimensions form square matrices. Must have a floating-point data type.
+
+-   **upper**: _bool_
+
+    -   If `True`, use the upper-triangular part to compute the eigenvalues and eigenvectors. If `False`, use the lower-triangular part to compute the eigenvalues and eigenvectors. Default: `False`.
+
+#### Returns
+
+-   **out**: _Tuple\[ &lt;array&gt; ]_
+
+    -   a namedtuple (`e`, `v`) whose
+    
+        -   first element must have shape `(..., M)` and consist of computed eigenvalues.
+        -   second element must have shape `(..., M, M)`and have the columns of the inner most matrices contain the computed eigenvectors.
+
+        Each returned array must have the same floating-point data type as `x`.
+
+```{note}
+
+Eigenvalue sort order is left unspecified.
+```
+
 (function-eigvalsh)=
 ### eigvalsh()
 

From a99df44c20baeda307584ab6b8cee8c9c6a0b92c Mon Sep 17 00:00:00 2001
From: Athan Reines <kgryte@gmail.com>
Date: Mon, 26 Apr 2021 02:25:27 -0700
Subject: [PATCH 2/2] Move API to submodule

---
 spec/API_specification/linear_algebra_functions.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/spec/API_specification/linear_algebra_functions.md b/spec/API_specification/linear_algebra_functions.md
index 597ad0d76..7348dc0b7 100644
--- a/spec/API_specification/linear_algebra_functions.md
+++ b/spec/API_specification/linear_algebra_functions.md
@@ -107,8 +107,8 @@ TODO
 
 TODO
 
-(function-eigh)=
-### eigh(x, /, *, upper=False)
+(function-linalg-eigh)=
+### linalg.eigh(x, /, *, upper=False)
 
 Returns the eigenvalues and eigenvectors of a symmetric matrix (or a stack of symmetric matrices) `x`.