linalg.trace(x, /, *, offset=0, dtype=None)[source]#

Returns the sum along the specified diagonals of a matrix (or a stack of matrices) x.

This function is Array API compatible, contrary to numpy.trace.

x(…,M,N) array_like

Input array having shape (…, M, N) and whose innermost two dimensions form MxN matrices.

offsetint, optional

Offset specifying the off-diagonal relative to the main diagonal, where:

* offset = 0: the main diagonal.
* offset > 0: off-diagonal above the main diagonal.
* offset < 0: off-diagonal below the main diagonal.
dtypedtype, optional

Data type of the returned array.


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:

out[i, j, k, ..., l] = trace(a[i, j, k, ..., l, :, :])

The returned array must have a data type as described by the dtype parameter above.

See also