tf.linalg.trace

Compute the trace of a tensor x.

tf.linalg.trace(
    x, name=None
)

trace(x) returns the sum along the main diagonal of each inner-most matrix in x. If x is of rank k with shape [I, J, K, ..., L, M, N], then output is a tensor of rank k-2 with dimensions [I, J, K, ..., L] where

output[i, j, k, ..., l] = trace(x[i, j, k, ..., l, :, :])

For example:

x = tf.constant([[1, 2], [3, 4]])
tf.linalg.trace(x)  # 5

x = tf.constant([[1, 2, 3],
                 [4, 5, 6],
                 [7, 8, 9]])
tf.linalg.trace(x)  # 15

x = tf.constant([[[1, 2, 3],
                  [4, 5, 6],
                  [7, 8, 9]],
                 [[-1, -2, -3],
                  [-4, -5, -6],
                  [-7, -8, -9]]])
tf.linalg.trace(x)  # [15, -15]

x tensor.
name A name for the operation (optional).

The trace of input tensor.