Scalar Vs Vector Vs Matrix Vs Tensor
Aspect | Scalar | Vector | Matrix | Tensor |
---|---|---|---|---|
Dimensionality | 0 | 1 | 2 | ≥ 3 |
Representation | Single numerical value | Ordered array of values | Two-dimensional array of values | Multidimensional array of values |
Usage | Represent basic quantities | Represent features, observations | Organize data in tabular format | Handle complex data structures |
Examples | Error metrics, probabilities | Feature vectors, gradients | Data matrices, weight matrices | Image tensors, sequence tensors |
Manipulation | Simple arithmetic operations | Linear algebra operations | Matrix operations, linear transformations | Tensor operations, deep learning operations |
Data Representation | Point in space | Direction and magnitude in space | Rows and columns in tabular format | Multi-dimensional relationships |
Applications | Basic calculations, statistical measures | Machine learning models, data representation | Data manipulation, statistical analysis | Deep learning, natural language processing |
Notation | Lowercase letters or symbols | Boldface letters or arrows | Uppercase boldface letters | Boldface uppercase letters or indices |
Difference Between Scalar, Vector, Matrix and Tensor
In the context of mathematics and machine learning, scalar, vector, matrix, and tensor are all different types of mathematical objects that represent different concepts and have different properties. Here in this article, we will discuss in detail scalars, vectors, matrixes, tensors, and finally the differences between them.
Table of Content
- What is Scalar?
- What are Vectors?
- What are Matrices?
- What are Tensors?
- Scalar Vs Vector Vs Matrix Vs Tensor