Update guidance on tuple field names (#203)

Author: kgryte

spec/extensions/linear_algebra_functions.md

@@ -200,10 +200,10 @@ Returns the eigenvalues and eigenvectors of a symmetric matrix (or a stack of sy
 
 -   **out**: _Tuple\[ <array> ]_
 
-    -   a namedtuple (`e`, `v`) whose
+    -   a namedtuple (`eigenvalues`, `eigenvectors`) 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.
+        -   first element must have the field name `eigenvalues` and must be an array consisting of computed eigenvalues. The array containing the eigenvalues must have shape `(..., M)`.
+        -   second element have have the field name `eigenvectors` and must be an array where the columns of the inner most matrices contain the computed eigenvectors. The array containing the eigenvectors must have shape `(..., M, M)`.
 
         Each returned array must have the same floating-point data type as `x`.
 
@@ -493,8 +493,8 @@ Computes the qr factorization of a matrix (or a stack of matrices), where `q` is
 
     -   a namedtuple `(q, r)` whose
 
-        -   first element must be an array whose shape depends on the value of `mode` and contain orthonormal matrices. If `mode` is `'complete'`, the array must have shape `(..., M, M)`. If `mode` is `'reduced'`, the array must have shape `(..., M, K)`, where `K = min(M, N)`. The first `x.ndim-2` dimensions must have the same size as those of the input `x`.
-        -   second element must be an array whose shape depends on the value of `mode` and contain upper-triangular matrices. If `mode` is `'complete'`, the array must have shape `(..., M, M)`. If `mode` is `'reduced'`, the array must have shape `(..., K, N)`, where `K = min(M, N)`. The first `x.ndim-2` dimensions must have the same size as those of the input `x`.
+        -   first element must have the field name `q` and must be an array whose shape depends on the value of `mode` and contain orthonormal matrices. If `mode` is `'complete'`, the array must have shape `(..., M, M)`. If `mode` is `'reduced'`, the array must have shape `(..., M, K)`, where `K = min(M, N)`. The first `x.ndim-2` dimensions must have the same size as those of the input `x`.
+        -   second element must have the field name `r` and must be an array whose shape depends on the value of `mode` and contain upper-triangular matrices. If `mode` is `'complete'`, the array must have shape `(..., M, M)`. If `mode` is `'reduced'`, the array must have shape `(..., K, N)`, where `K = min(M, N)`. The first `x.ndim-2` dimensions must have the same size as those of the input `x`.
 
         Each returned array must have a floating-point data type determined by {ref}`type-promotion`.
 
@@ -520,8 +520,8 @@ The purpose of this function is to calculate the determinant more accurately whe
 
     -   a namedtuple (`sign`, `logabsdet`) whose
 
-        -   first element must be an array containing a number representing the sign of the determinant for each square matrix.
-        -   second element must be an array containing the determinant for each square matrix.
+        -   first element must have the field name `sign` and must be an array containing a number representing the sign of the determinant for each square matrix.
+        -   second element must have the field name `logabsdet` and must be an array containing the determinant for each square matrix.
 
         For a real matrix, the sign of the determinant must be either `1`, `0`, or `-1`. If a determinant is zero, then the corresponding `sign` must be `0` and `logabsdet` must be `-infinity`. In all cases, the determinant must be equal to `sign * exp(logsabsdet)`.
 
@@ -569,9 +569,9 @@ Computes the singular value decomposition `A = USV` of a matrix (or a stack of m
 
     -   a namedtuple `(u, s, v)` whose
 
-        -   first element must be an array whose shape depends on the value of `full_matrices` and contain unitary array(s) (i.e., the left singular vectors). The left singular vectors must be stored as columns. If `full_matrices` is `True`, the array must have shape `(..., M, M)`. If `full_matrices` is `False`, the array must have shape `(..., M, K)`, where `K = min(M, N)`. The first `x.ndim-2` dimensions must have the same shape as those of the input `x`.
-        -   second element must be an array with shape `(..., K)` that contains the vector(s) of singular values of length `K`. For each vector, the singular values must be sorted in descending order by magnitude, such that `s[..., 0]` is the largest value, `s[..., 1]` is the second largest value, et cetera. The first `x.ndim-2` dimensions must have the same shape as those of the input `x`.
-        -   third element must be an array whose shape depends on the value of `full_matrices` and contain unitary array(s) (i.e., the right singular vectors). The right singular vectors must be stored as rows (i.e., the array is the adjoint). If `full_matrices` is `True`, the array must have shape `(..., N, N)`. If `full_matrices` is `False`, the array must have shape `(..., K, N)` where `K = min(M, N)`. The first `x.ndim-2` dimensions must have the same shape as those of the input `x`.
+        -   first element must have the field name `u` and must be an array whose shape depends on the value of `full_matrices` and contain unitary array(s) (i.e., the left singular vectors). The left singular vectors must be stored as columns. If `full_matrices` is `True`, the array must have shape `(..., M, M)`. If `full_matrices` is `False`, the array must have shape `(..., M, K)`, where `K = min(M, N)`. The first `x.ndim-2` dimensions must have the same shape as those of the input `x`.
+        -   second element must have the field name `s` and must be an array with shape `(..., K)` that contains the vector(s) of singular values of length `K`. For each vector, the singular values must be sorted in descending order by magnitude, such that `s[..., 0]` is the largest value, `s[..., 1]` is the second largest value, et cetera. The first `x.ndim-2` dimensions must have the same shape as those of the input `x`.
+        -   third element must have the field name `v` and must be an array whose shape depends on the value of `full_matrices` and contain unitary array(s) (i.e., the right singular vectors). The right singular vectors must be stored as rows (i.e., the array is the adjoint). If `full_matrices` is `True`, the array must have shape `(..., N, N)`. If `full_matrices` is `False`, the array must have shape `(..., K, N)` where `K = min(M, N)`. The first `x.ndim-2` dimensions must have the same shape as those of the input `x`.
 
         Each returned array must have the same floating-point data type as `x`.