Can Vector Units Be Simplified or Must Each Element Carry Units?

[sandy.bridge]

If I have a vector defining numerous quantities of the same units, can I merely place the units outside of the vector, or is it required to have units on every entity within the vector?

For example,
$$(A, B, C)=(ae^{j\phi_1}, be^{j\phi_2}, ce^{j\phi_3}) H$$
or
$$(A, B, C)=(ae^{j\phi_1} H, be^{j\phi_2} H, ce^{j\phi_3} H)$$

 

[jedishrfu]

My two cents is for clarity place the units of measure inside. Its not a factor.

For example, a position vector r=<1.0m,2.0m,3.0m> is much clearer than <1.0,2.0,3.0> m as someone might think its some undefined constant.

 

[sandy.bridge]

Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?

 

[jedishrfu]

Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?

I can't answer for mathematicians but ( ) are usually for expressions, <> for vectors and [ ] intervals.

But I did find this:

http://en.wikipedia.org/wiki/List_of_mathematical_symbols

which may answer your questions.

 

[NemoReally]

You can place the unit outside of the delimiter - see, for example, http://physics.nist.gov/Pubs/SP811/sec07.html section 7.7 (I believe the SP811 follows the ISO 31000 series in this respect)

 

[jedishrfu]

You can place the unit outside of the delimiter - see, for example, http://physics.nist.gov/Pubs/SP811/sec07.html section 7.7 (I believe the SP811 follows the ISO 31000 series in this respect)

Nice article, I would still question this for a vector although I did see a list of values in parens with the uom at the end as the preferred list method.

 

[NemoReally]

Nice article, I would still question this for a vector although I did see a list of values in parens with the uom at the end as the preferred list method.

International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
3rd edition

http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf

1 Quantities and units
1.1 (1.1)
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference
NOTE 5 A quantity as defined here is a scalar. However, a vector or a tensor, the components of which are quantities, is also considered to be a quantity.

1.19 (1.18)
quantity value
value of a quantity
value
number and reference together expressing magnitude of a quantity
NOTE 4 In the case of vector or tensor quantities, each component has a quantity value.
EXAMPLE Force acting on a given particle, e.g. in Cartesian components (Fx; Fy; Fz) = (-31.5; 43.2; 17.0) N.

... if it's good enough for the BIPM and ISO, it's good enough for me.

 

[jedishrfu]

International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
3rd edition

http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2012.pdf

1 Quantities and units
1.1 (1.1)
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference
NOTE 5 A quantity as defined here is a scalar. However, a vector or a tensor, the components of which are quantities, is also considered to be a quantity.

1.19 (1.18)
quantity value
value of a quantity
value
number and reference together expressing magnitude of a quantity
NOTE 4 In the case of vector or tensor quantities, each component has a quantity value.
EXAMPLE Force acting on a given particle, e.g. in Cartesian components (Fx; Fy; Fz) = (-31.5; 43.2; 17.0) N.

... if it's good enough for the BIPM and ISO, it's good enough for me.

Yup, that nails it. Good to know. Thanks.

Also they suggest using ; instead of ,

 

[HallsofIvy]

Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?

I can't answer for mathematicians but ( ) are usually for expressions, <> for vectors and [ ] intervals.

Speaking for mathematicians, the real problem is that points are represented, in a Cartesian coordinate system, as (x, y, z), writing vectors as <a, b, c> is less confusing that using (a, b, c).