You just used “tensor” to define “tensor,” but also any list of number formulated as an n-dimensional matrix will satisfy this criterion. A tensor is both a linear transformation and an n-dimensional box-shaped list of numbers, but there’s nothing such as a linear list of numbers.
“Linear” describes transformations, not numbers.
Isn’t a tensor a multilinear map taking as input a tensor and outputting another tensor?
Also, but that is because math likes to reuse names like Donald Duck reuses his jacket…
You just used “tensor” to define “tensor,” but also any list of number formulated as an n-dimensional matrix will satisfy this criterion. A tensor is both a linear transformation and an n-dimensional box-shaped list of numbers, but there’s nothing such as a linear list of numbers.