How do I go about this?

[JohnW2]

A vector can be considered as a 1-column, or 1-row matrix, giving a column or row vector. The dimension is the numbers of components in the vector, any number in theory but mostly 2 or 3 in practice.

It sounds as if I've used the word "dimension" incorrectly per a mathematician's definition - I either never knew or have forgotten that the mathematical meaning was such as you indicate. By analogy with the language used for data structures (see below) when I spoke of a 'one-dimensional matrix', I was talking about a 1-column (or 1-row) matrix.

You can do matrix algebra with them. I just did it on Mathcad, made a 3x3 matrix M, and 3-component row and column vectors, Vr and Vc. It only works with M*Vc or Vr*M, not vice-versa.

Fair enough.

I don't know anything about 'R' so can't comment.

It's not just 'R', but is similar in quite a few programming languages. Data structures (generally "arrays") usually use "dimension" in the 'everyday' sense, with a 1-dimensional array (just a list of components - aka 1-row or 1-column) often called a "vector" and a 2-dimensional array representing an R x C table/array/matrix of values. In terms of data structures, N-dimensional arrays are perfectly possible (and common), but I don't know whether mathematicians have any equivalent with matrices (if they do, they would be well above my head!)!

I'm having to dredge the memory banks here, but I don't think you can treat electrical quantities as vector which has both magnitude and direction.

As I've said, in engineering etc. circles a "vector" quantity is simply one which has both magnitude and direction, so the language gets a bit confusing. However ...

Eg with complex impedance Z = R + jwL I = V/Z = V/(R+jwL) = V*(R-jwL)/((R+jwL)*(R-jwL)) = V*(R-jwL)/(R^2+L^2*w^2). I don't see how you can do that with vectors, unless you're an electrician to whom a vector is a complex number!

I think I may be seeing your point. Given two 'vector quantities' (i.e. two magnitudes and the angle between them) one can undertake 'vector addition' and 'vector subtraction' just by using trig. However, I'm not aware of whether/how one can do that (I rather doubt it) with any mathematical operations other than addition and subtraction, although one can with complex numbers.

 

[fixitflav]

It sounds as if I've used the word "dimension" incorrectly per a mathematician's definition - I either never knew or have forgotten that the mathematical meaning was such as you indicate. By analogy with the language used for data structures (see below) when I spoke of a 'one-dimensional matrix', I was talking about a 1-column (or 1-row) matrix.

Fair enough.

It's not just 'R', but is similar in quite a few programming languages. Data structures (generally "arrays") usually use "dimension" in the 'everyday' sense, with a 1-dimensional array (just a list of components - aka 1-row or 1-column) often called a "vector" and a 2-dimensional array representing an R x C table/array/matrix of values. In terms of data structures, N-dimensional arrays are perfectly possible (and common), but I don't know whether mathematicians have any equivalent with matrices (if they do, they would be well above my head!)!

As I've said, in engineering etc. circles a "vector" quantity is simply one which has both magnitude and direction, so the language gets a bit confusing. However ...

I think I may be seeing your point. Given two 'vector quantities' (i.e. two magnitudes and the angle between them) one can undertake 'vector addition' and 'vector subtraction' just by using trig. However, I'm not aware of whether/how one can do that (I rather doubt it) with any mathematical operations other than addition and subtraction, although one can with complex numbers.

I'm off on holiday tomorrow for a few days so probably won't log on. But I think we've pretty much exhausted this, it's been an interesting chat!

 

[JohnW2]

I'm off on holiday tomorrow for a few days so probably won't log on. But I think we've pretty much exhausted this, it's been an interesting chat!

It has, even if it's bored others silly. As I've tried explaining, the important thing for the OP to realise (if he's still around!) is that the sort of maths we've been talking about are way way beyond anything that a domestic electrician would ever have to know about.

I hope you have a great holiday!
Cheers,
John