2019年10月17日 · $\begingroup$ I have also used the term "conjugate" as a verb: to conjugate (v.) an expression is to multiply it by its conjugate (n.). $\endgroup$ – Andrew Chin Commented Oct 17, 2019 at 4:58

2019年10月31日 · The word conjugate itself comes from Latin and means (literally) "to yoke together", and the idea behind the word is that the things that are conjugate are somehow bound to each other. In (most European) languages verbs are conjugated by tying endings to the infinitival stem, and in mathematics things are conjugate when they are somehow bound ...

2016年10月17日 · Finally for now, conjugate elements in a group always have the same order (since conjugation by an element of the group is an automorphism). This comes in handy when working with group presentations, among other things. For instance when two elements are conjugate and have relatively prime order, they are the identity element.

You have a number $\sqrt{x}+2\sqrt{b}$ and you're asking for the conjugate. Most times this refers to the complex conjugate, which involves replacing the imaginary part of the complex number with its negative. Your number is a purely real number, so its complex conjugate is itself.

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2013年10月12日 · I was confused by this too. The word conjugate is quite an overloaded one in Math. The plain English definition of the word is hard enough to follow and seems to bear little intuitive relationship to the various Mathematical concepts. Anyway: The concept of conjugate vectors is closely related to orthogonal vectors and linearly independence of ...

This tells us that the conjugate of any matrix gives a new matrix which represents the same linear map (so the action on the group is of exactly the same type. Even though it will now map the same vector to a different one as the preconjugated matrix, if you write the original vector in terms of the new basis, the new matrix will map it to the ...

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So I understand that something like $4-i$ is a complex conjugate of $4+i$, however are things like; (a) $-4+i = \overline{-4-i}$, (b) $-4+i = \overline{4+i}$, and (c) $-4-i = \overline{4+i}$. Generally am I allowed to say an reflection of a complex number about the x, y, or both axis is a conjugate of the original number? Thanks.

2017年3月16日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.