this post was submitted on 21 Aug 2025
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I mean... it also has to be linear too, but sure okay ☺️
What has to be linear? Vector?matrix? Tensor? Neither makes sense
You lost me at vectors not having to be linear. You can apply nonlinear functions or operations to vectors, but doing so transforms them into a different, non-linear context, afaik. We might be using different definitions of some of these terms, especially "linear".
"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.