Where

  T  is  a  list.  Where List can contain different data types within a single list

  Z  is   a z List  ( scalar , vector , matrix etc )

If T is  List  then  function F is not defined from T to Z. 

Where

  T  is  a  Numpy ndarray.  Ndarray  is a multidimensional or n-dimensional array of fixed size with homogeneous elements( i.e., the data type of all the elements in the array is the same). NumPy for working with an array. NumPy  support CPU and also no automatic Differentiation.  Values can be numerical. These arrays used in Scipy,sklearn,xgboost, and lightgbm. These are Machine Learning Platforms. .   

  Z  is   a Tensor  or  Numpy Ndarray. ( it can be  Scalar, Vector, Matrix  , Tensor etc)

If T is Numpy.ndarray then  function F is not defined from T to Z. 

To do mathematics  with Numpy

new create  : array_ = np.array([1,2,3])

Sum per row : np.sum(array_, axis=1)

multiplicaiton :np.matmul(array_a, array_b)

divide items elementwise : np.divide(array_a, array_b)

add items elementwise : np.add(array_a, array_b)

subtract items elementwise : np.subtract(array_a, array_b)

reshape item: np.reshape(array_, (1,2))

shape of item : array_.shape

Where

  T  is  a Tensor. Tensor is a multidimensional array with a uniform data type as dtype. Update a tensor is not defined   but create a new one. TensorFlow for working with a tensor.  If  TensorFlow library is used for tensor then TensorFlow decide when to use GPU or when to use CPU as the TensorFlow library automatically takes care of that. TensorFlow support CPU/GPU/TPU and also automatic Differentiation.  Values can be numerical / Strings. do not try to append, insert, delete or change a value to a tensor. Tensors used in TensorFlow and also in PyTorch ( these two are Deep  Learning platforms )

  Z  is   a Tensor ( it can be  Scalar, Vector, Matrix  , Tensor etc)

 F is a function from Tensor T to another Tensor Z.

Since Function F is defined on Tensor T, it is possible to compute Derivative of T.  ( GPU is very useful to compute Derivative of F)

To do mathematics with  TensorFlow version of Tensor

new create  : tensor_ = tf.constant([1,2,3])

Sum per row : tf.reduce_sum(tensor_, reduction_indices=[1])

multiplicaiton : tf.matmul(tensor_a, tensor_b)

divide items elementwise : tf.div(tensor_a, tensor_b)

add items elementwise : tf.add(tensor_a, tensor_b)

subtract items elementwise : tf.subtract(tensor_a, tensor_b)

reshape item: tf.reshape(tensor_, (1,2))

shape of item : tensor_.get_shape()

Use of Tensor to represent Data is a good option. Above shows it is not good to use numpy.ndarray to represent Data.  A tensor is a more suitable choice if GPU is available for computing.   tensor  can reside in  GPU accelerators memory. Tensors are immutable