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Wondering what words you could use to describe the following Matrix properties.

The prefix eigen- is adopted from the German word eigen for "proper", "characteristic".

So that word is basically "matrix property" or "matrix attribute", which is rather generic.

The rest of the matrix terms for the most part make sense to me (inverse, skew, rotation, orthogonal, etc.).

After reading through the above definitions though, these words don't offer any visualization help. Wondering if there are any other words for these things that make it easier to understand, remember, or visualize.

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    $\begingroup$ Why do you want to change the standard words for these things by other words? Saying "stol" instead of "four" does not change the essential properties of the notion $\bullet\bullet\bullet\bullet$. $\endgroup$ – Christian Blatter Mar 10 '19 at 18:57
  • $\begingroup$ Mathematical ideas are often complicated, which requires the introduction of specialized language to deal with them (this is true in any field, by the way---the terms phone, phoneme, allophone, morpheme, etc are words which are difficult to keep separate, but which have distinct meaning in descriptive linguistics). Rather than demand that mathematicians come up with more "intuitive" language (which is actually likely to muddle things even more, as intuitive language can give rise to false friends), it might be better to just learn the definitions. $\endgroup$ – Xander Henderson Mar 11 '19 at 3:44
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I won't try to give explanations for all of the terms here, but the short answer is "we have good reasons (perhaps sometimes only historical) to call things what we call them".

Take for instance, why we call determinants determinants. We had been discussing interesting properties of linear systems for a longer time than we had a good grasp on matricies, and the use of the word grew from a long history of math.

Other than a bunch of deep dives into the history of math to answer your question in full, the comment on your post sums it up quite nicely; why change what we are using in a purely notational way unless you can present a clear and obvious advantage to the new notation? Simply renaming determinants to quasiflopkins does little to illuminate the situation, and as confusing as determinants are to learn there is a reason that they are called that.

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