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

[J-dizzal]

Could anyone clarify what is the name of the i,j,k notation for vectors if there even is one?

 

[anorlunda]

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.

 

[J-dizzal]

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.

 

[anorlunda]

Not that I know.

 

[rootone]

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).

 

[J-dizzal]

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".