What does the asterisk mean?

Author: Xuan Jr.

Review: Tianyang.

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USTC has a strange tradition: there is an asterisk (*) after the name of each female student on all call books of the undergraduate.

Somebody once told me that this * means conjugate transpose.

But, you know, it is so absurd.

Today noon when I got up, I suddenly came up with a romantic explanation.

This *, possibly means duality.

All boys constitute a vector space.

All girls constitute a vector space.

These two spaces are dual space of each other.

Each element of the first vector space has a corresponding element in the second vector space.

Each element of the second vector space has a corresponding element in the first vector space.

These two elements are dual elements of each other.

And this dual relationship exists from birth (命中注定), exists forever (白头偕老) and never changes (从一而终).

It is so romantic, isn’t it?

From the point of a physicist, you can consider the elements of the first vector space as column vectors and the elements of the second vector space as row vectors.

In the literature of tensor, column vectors are (1,0) tensors while row vectors are (0,1) tensors.

By the way, a row vector is also called a co-vector.

For more details about duality space, please refer to Wikipedia, Zhihu, etc.

Well, to tell you the truth, conjugate transpose and duality depict the same thing.

However, for the same asterisk:

If you translate it into conjugate transpose or Hermite, then you are such a stupid fool.

If you translate it into duality, then you are such a breathless romanticer.

The most romantic part of this story is: when two dual elements combine with each other, they will map the other into $R$.

It just like, they have a baby!