Understanding Vector Notation: The Role of i, j, and k as Standard Unit Vectors

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Discussion Overview

The discussion revolves around the notation of vectors using the symbols i, j, and k, particularly in the context of their roles as standard unit vectors in three-dimensional space. Participants seek to clarify whether there is a formal name for this notation and explore its conventions and usage in mathematical contexts.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asks for the formal name of the i, j, k notation used for vectors.
  • Another participant suggests that i, j, k are commonly used letters in mathematical notation attributed to Leonhard Euler, but does not provide a specific name for the notation itself.
  • A participant mentions that their professor refers to the notation as "i, j, k notation" but is curious if there is a more accepted term.
  • Some participants express that i represents an integer and suggest that using j, k, l, etc., makes notation clearer when more integers are needed.
  • There is mention of a professor referring to the notation as "index notation," but this is not universally agreed upon.

Areas of Agreement / Disagreement

Participants generally agree that i, j, and k correspond to the x, y, and z axes, respectively. However, there is no consensus on a formal name for the notation, with multiple views and some uncertainty expressed regarding its terminology.

Contextual Notes

Participants have not reached a clear agreement on the formal naming of the i, j, k notation, and there are varying interpretations of its use and meaning in different contexts.

J-dizzal
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Could anyone clarify what is the name of the i,j,k notation for vectors if there even is one?
 
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I'm not sure what you're really asking, but the letters I, j ,k, l, m, and n are commonly used in all mathematical notation to represent integer values. It is just a convention that is attributed to Leonhard Euler.
 
anorlunda said:
I'm not sure what you're really asking, but the letters I, j ,k, l, m, and n are commonly used in all mathematical notation to represent integer values. It is just a convention that is attributed to Leonhard Euler.

For example, if you were asked to put the components of a vector from ℝ3 in terms of the unit vectors i, j, and k what is that notation called? My professor calls it "i,j,k notation" I am wondering if there is a formal or standard name.
 
Not that I know.
 
Afaik, 'i' is just a simple shorthand notation symbolising an 'integer'.
If you need more than one integer to write some algorithm it's just a bit more 'understandable' to use j.k.l etc for the additional integers.
You could use i1, i2,i3 instead as symbols representing the same quantity, but that just makes thing more difficult to comprehend (imo).
 
rootone said:
Afaik, 'i' is just a simple shorthand notation symbolising an 'integer'.
If you need more than one integer to write some algorithm it's just a bit more 'understandable' to use j.k.l etc for the additional integers.
You could use i1, i2,i3 instead as symbols representing the same quantity, but that just makes thing more difficult to comprehend (imo).

yea i agree. But there seems to be some agreement that standard unit vectors i, j, and k correspond respectively to the x, y, and z axes. Because they are standard unit vectors i thought there would be an accepted name to describe a vector in i,j,k notation rather than just say i,j,k notation.

Ive heard one professor refer ## \hat i, \hat j, \hat k ## notion as "index notation".
 
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