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abrowaqas
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Can we call a vector as Tensor, discuss What is different between Vector and Tensor? What happens if we permute the subscript of tensors
abrowaqas said:i got the idea about tensors... so that means tensors are the combination of both vectors and scalars ... tensor become scalar when n= 0 in 3^n otherwise a tensor is a scalar .. am i right... but what if we permute the tensor... i read in one of the source it says that if you permute the subcript of tensor you will get another new tensor. but didn't explain the idea.. so if you have idea .. kindly share
A vector is a mathematical object that has both magnitude and direction, represented by an arrow. It can be described as a quantity that has both size and direction. A tensor, on the other hand, is a mathematical object that describes the relationship between vectors and other tensors. It is a multidimensional array of numbers that can represent physical quantities such as forces, stresses, and strains.
A vector has three components in three-dimensional space, while a tensor can have multiple components, depending on the number of dimensions. For example, a tensor in three-dimensional space has nine components, while a tensor in four-dimensional space has sixteen components.
Yes, a vector can be considered as a special case of a tensor. A vector is a rank-1 tensor, meaning that it has one dimension. In contrast, a tensor can have any number of dimensions, including one, making a vector a special case of a tensor.
A vector is typically represented by a single letter with an arrow on top, such as v. In contrast, a tensor is represented by multiple letters, each representing a different dimension, such as Tij for a two-dimensional tensor.
Vectors and tensors have many practical applications in various fields, including physics, engineering, computer graphics, and machine learning. For example, vectors are used to represent physical quantities like velocity and acceleration, while tensors are used to describe physical properties like stress and strain in materials. In computer graphics, vectors are used to represent the direction and intensity of light, while tensors are used to model the deformation of objects. In machine learning, tensors are used to represent data and parameters in deep learning models.