Why isn't conjugate transpose used as a default sign for transposition?

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When I'm looking at definitions/articles, etc., for real matrices the sign for transposition is upperscore T, while when a defintion for complex matrices/vector spaces, the sign for transposition is upperscore * (conjugate transpose). As you can use either for real matrices, why isn't the * used everywhere? What is the purpose of "splitting" the definitons like that?