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Remove axisN eyword arguments from linalg.diag and linalg.trace (#241)
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‎spec/extensions/linear_algebra_functions.md

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@@ -140,23 +140,15 @@ Returns the determinant of a square matrix (or stack of square matrices) `x`.
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- if `x` is a two-dimensional array, a zero-dimensional array containing the determinant; otherwise, a non-zero dimensional array containing the determinant for each square matrix. The returned array must have the same data type as `x`.
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(function-linalg-diagonal)=
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### linalg.diagonal(x, /, *, axis1=0, axis2=1, offset=0)
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### linalg.diagonal(x, /, *, offset=0)
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Returns the specified diagonals. If `x` has more than two dimensions, then the axes (dimensions) specified by `axis1` and `axis2` are used to determine the two-dimensional sub-arrays from which to return diagonals.
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Returns the specified diagonals of a matrix (or a stack of matrices) `x`.
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#### Parameters
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- **x**: _<array>_
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- input array. Must have at least `2` dimensions.
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- **axis1**: _int_
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- first axis (dimension) with respect to which to take diagonal. Default: `0`.
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- **axis2**: _int_
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- second axis (dimension) with respect to which to take diagonal. Default: `1`.
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- input array having shape `(..., M, N)` and whose innermost two dimensions form `MxN` matrices.
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- **offset**: _int_
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@@ -172,7 +164,7 @@ Returns the specified diagonals. If `x` has more than two dimensions, then the a
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- **out**: _<array>_
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- if `x` is a two-dimensional array, a one-dimensional array containing the diagonal; otherwise, a multi-dimensional array containing the diagonals and whose shape is determined by removing `axis1` and `axis2` and appending a dimension equal to the size of the resulting diagonals. The returned array must have the same data type as `x`.
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- an array containing the diagonals and whose shape is determined by removing the last two dimensions and appending a dimension equal to the size of the resulting diagonals. The returned array must have the same data type as `x`.
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(function-linalg-eig)=
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### linalg.eig()
@@ -593,23 +585,15 @@ Computes the singular values of a matrix (or a stack of matrices) `x`.
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- 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`. The returned array must have the same floating-point data type as `x`.
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(function-linalg-trace)=
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### linalg.trace(x, /, *, axis1=0, axis2=1, offset=0)
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### linalg.trace(x, /, *, offset=0)
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Returns the sum along the specified diagonals. If `x` has more than two dimensions, then the axes (dimensions) specified by `axis1` and `axis2` are used to determine the two-dimensional sub-arrays for which to compute the trace.
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Returns the sum along the specified diagonals of a matrix (or a stack of matrices) `x`.
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#### Parameters
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- **x**: _<array>_
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- input array. Must have at least `2` dimensions. Should have a numeric data type.
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- **axis1**: _int_
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- first axis (dimension) with respect to which to compute the trace. Default: `0`.
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- **axis2**: _int_
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- second axis (dimension) with respect to which to compute the trace. Default: `1`.
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- input array having shape `(..., M, N)` and whose innermost two dimensions form `MxN` matrices. Should have a numeric data type.
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- **offset**: _int_
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@@ -625,9 +609,7 @@ Returns the sum along the specified diagonals. If `x` has more than two dimensio
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- **out**: _<array>_
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- if `x` is a two-dimensional array, the returned array must be a zero-dimensional array containing the trace; otherwise, the returned array must be a multi-dimensional array containing the traces.
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The shape of a multi-dimensional output array is determined by removing `axis1` and `axis2` and storing the traces in the last array dimension. For example, if `x` has rank `k` and shape `(I, J, K, ..., L, M, N)` and `axis1=-2` and `axis1=-1`, then a multi-dimensional output array has rank `k-2` and shape `(I, J, K, ..., L)` where
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- an array containing the traces and whose shape is determined by removing the last two dimensions and storing the traces in the last array dimension. For example, if `x` has rank `k` and shape `(I, J, K, ..., L, M, N)`, then an output array has rank `k-2` and shape `(I, J, K, ..., L)` where
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```text
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out[i, j, k, ..., l] = trace(a[i, j, k, ..., l, :, :])

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