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enter image description here

Assume I haven't seen this figure before and I want to learn about eigendecomposition intuitively and visually.

Is it clear and idiomatic to ask that what does eigendecomposition look like?

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If your goal is to see the graphical or visual representation of a concept, you should ask for that specifically. "What does it look like" in this context isn't as clear as you want-- "look" is often used is various metaphorical ways and this phrasing is also a casual way of asking for a (textual) explanation of the nature of something (e.g. "Doctor, I can't figure out what's wrong with me, what does it look like to you?")

There may be a more technical math-specific way of referring to the graph of a function or process (I'm not a mathematician) but I think if you asked "what does the graphical representation of eigendecomposition look like", it would be clear and idiomatic.

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