The general idea of a tensor is an array of values:
• A 0-dimensional tensor is just a single value, called a "scalar"
• A 1-dimensional tensor is a vector
• A 2-dimensional tensor is a matrix
• A 3-dimensional tensor is like a matrix with an extra dimension
etc.
AND a tensor usually has all values linked somehow, so the tensor obeys transformation rules such as being able to be rotated or scaled.
Examples:
• in physics a tensor can show the amount and direction of stress throughout an object
• in machine learning a tensor can show the values at nodes in a neural network
Definition of