# Tensor Ranks, Shapes, and Types

TensorFlow programs use a tensor data structure to represent all data. You can think of a TensorFlow tensor as an n-dimensional array or list. A tensor has a static type and dynamic dimensions. Only tensors may be passed between nodes in the computation graph.

## Rank

In the TensorFlow system, tensors are described by a unit of dimensionality known as rank. Tensor rank is not the same as matrix rank. Tensor rank (sometimes referred to as order or degree or n-dimension) is the number of dimensions of the tensor. For example, the following tensor (defined as a Python list) has a rank of 2:

t = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]


A rank two tensor is what we typically think of as a matrix, a rank one tensor is a vector. For a rank two tensor you can access any element with the syntax t[i, j]. For a rank three tensor you would need to address an element with t[i, j, k].

Rank Math entity Python example
0 Scalar (magnitude only) s = 483
1 Vector (magnitude and direction) v = [1.1, 2.2, 3.3]
2 Matrix (table of numbers) m = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
3 3-Tensor (cube of numbers) t = [[[2], [4], [6]], [[8], [10], [12]], [[14], [16], [18]]]
n n-Tensor (you get the idea) ....

## Shape

The TensorFlow documentation uses three notational conventions to describe tensor dimensionality: rank, shape, and dimension number. The following table shows how these relate to one another:

Rank Shape Dimension number Example
0 [] 0-D A 0-D tensor. A scalar.
1 [D0] 1-D A 1-D tensor with shape [5].
2 [D0, D1] 2-D A 2-D tensor with shape [3, 4].
3 [D0, D1, D2] 3-D A 3-D tensor with shape [1, 4, 3].
n [D0, D1, ... Dn-1] n-D A tensor with shape [D0, D1, ... Dn-1].

Shapes can be represented via Python lists / tuples of ints, or with the tf.TensorShape.

## Data types

In addition to dimensionality, Tensors have a data type. You can assign any one of the following data types to a tensor:

Data type Python type Description
DT_FLOAT tf.float32 32 bits floating point.
DT_DOUBLE tf.float64 64 bits floating point.
DT_INT8 tf.int8 8 bits signed integer.
DT_INT16 tf.int16 16 bits signed integer.
DT_INT32 tf.int32 32 bits signed integer.
DT_INT64 tf.int64 64 bits signed integer.
DT_UINT8 tf.uint8 8 bits unsigned integer.
DT_UINT16 tf.uint16 16 bits unsigned integer.
DT_STRING tf.string Variable length byte arrays. Each element of a Tensor is a byte array.
DT_BOOL tf.bool Boolean.
DT_COMPLEX64 tf.complex64 Complex number made of two 32 bits floating points: real and imaginary parts.
DT_COMPLEX128 tf.complex128 Complex number made of two 64 bits floating points: real and imaginary parts.
DT_QINT8 tf.qint8 8 bits signed integer used in quantized Ops.
DT_QINT32 tf.qint32 32 bits signed integer used in quantized Ops.
DT_QUINT8 tf.quint8 8 bits unsigned integer used in quantized Ops.