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

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SUMMARY

The discussion centers on the notation of vectors in three-dimensional space, specifically the use of unit vectors i, j, and k. These vectors are standard representations for the x, y, and z axes, respectively, and are attributed to the conventions established by mathematician Leonhard Euler. While commonly referred to as "i, j, k notation," some educators also describe this as "index notation," particularly when denoting unit vectors as \hat i, \hat j, and \hat k. The consensus indicates that this notation enhances clarity when expressing vector components.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with three-dimensional coordinate systems
  • Basic knowledge of mathematical notation conventions
  • Awareness of historical contributions by mathematicians like Leonhard Euler
NEXT STEPS
  • Research the formal definitions and applications of unit vectors in physics and engineering
  • Explore the concept of index notation in advanced mathematics
  • Learn about vector operations in three-dimensional space, including addition and scalar multiplication
  • Investigate the historical context of mathematical notation and its evolution
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Students and professionals in mathematics, physics, and engineering who seek to deepen their understanding of vector notation and its applications in three-dimensional analysis.

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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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