Understanding Tensor (1): Dimension
1.First of all
Organize the information you need to understand Tensor as your own notes. At the same time, I will introduce the Tensor notation in Python.
- Since the English expressions are intuitive and easy to understand, I will write them as they are without translating them.
2. What is a tensor?
- Tensor is a just a container for data.
- The data are almost numerical data
- Therefore, Tensor is a container for number.
A tensor is a container that holds numbers. It's simple. There are various explanations about tensors as shown in the figure below, but the point is ** a container to put numbers **.
3. Tensor keywords
It means Tensor, Dimension, Axis, Ranks.
- Tensor is a container of numbers.
- Tensor is a generalization of matrices to an arbitrary number of dimensions.
- In tensor, dimension is often called axis.
- Number of dimension (=Number of axis) is called ranks.
A tensor is a generalized representation of the matrix.
| name | tensor | Notation |
|---|---|---|
| Scalar | 0 Dimensional Tensor | Not Available |
| Vector | 1 Dimensional Tensor | (k) |
| Matrix | 2 Dimensional Tensor | (j,k) |
| .. | 3 Dimensional tensor | (i,j,l) |
4. Tensor Dimension
Here's an example of a tensor, how to fill in Python. Python uses ** [] ** to represent lists. Let's get used to this expression quickly. You can check the Dimension of Tensor with the ndmi command of numpy.
4.1 Scalar : 0D Tensor A tensor that contains only one number is called a scalar.
4.2 Vector : 1D Tensor
An array of number is called a vector, or 1D tensor.
4.3 Matrix : 2D Tensor
An array of vecotrs is a matrix, or 2D tensor.
4.4 .. :3D Tensor
It is just nD tensor from 3D tensor.
5. Summary
A tensor is a container that holds numbers. I organized the meaning of Dimension (= axis) of Tensor and the expression in Python. Next time, I will introduce Tensor's Shape.