The discussion revolves around the classification of scalar quantities, specifically whether complex numbers can be considered scalars alongside real numbers. Participants explore the definitions and implications of scalars in various mathematical contexts.
Participants express differing views on the classification of complex numbers as scalars, with no consensus reached on the definitions or implications of scalars in various mathematical contexts.
The discussion highlights potential ambiguities in the definitions of scalars, particularly regarding the inclusion of units and the dimensionality of the quantities involved. The context of scalar quantities may vary depending on mathematical or physical frameworks.
Scalars are numbers, rationals, reals, complex or even quaternions. Units are not part of them! A unit is a special measure of a dimension like length or weight. Scalars are dimensionless.topito2 said:I was taught a scalar is a quantity that consists of a number (positive or negative) and it might include a measuring unit, e.g. 6, 5 kg, -900 J, etc. I was wondering if complex numbers like 3 + 7j (where j is the square root of minus 1) can be considered scalar quantities too, or is it that only real numbers (that might include measuring units) can be considered scalars?
Can you tell which direction?topito2 said:Thank you so much for the speedy reply, guys! BTW, could you please provide any reference (book or website) I could check to dig a little bit more on the subject?