Understanding Linear Algebra and the Kanji for “Linear”

One of the mathematics studied in university is “llinear algebra.” It is a mathematics that uses matrices and vector spaces, and there have been many books on linear algebra published to date. In these books, two different kanji characters are used for “linear.”

The Japanese translations for “linear” are “線型” and “線形,” but some people may wonder what the difference between these two is.

It is the difference between “type” or “shape” of a line.

In cases like linear transformations, linear mappings, linear forms, and linear independence, these concepts are related to a straight “type,” so “線型” would be appropriate.

Personal Preferences and Trends in Usage

Additionally, “linear” gives a sense of being straight, and it can also be translated as “one dimension,” so “linear transformation” and “one-transformation,” “linear mapping” and “one-mapping,” “linear form” and “one-form,” and “linear independence” and “one-independence” all mean the same thing.

You probably don’t need to worry too much about it, but there are people who dislike the use of “線形” (I am one of them). However, compared to several decades ago, it seems that “線形” has become more widely used nowadays… 🙁