Thanks, Are you a faculty member of British Columbia U ?

John, Thanks. I ended breaking down and just doing the multiplications explicitly by myself like you suggested. However I didn't create any fancy procedures like you did. So, there are practically no built-in Maple procedures for using commutator/anitcommutator relations on matrix data types in Maple...? I'm also surprised. Thanks again. v/r, Dan

John, Thanks. I ended breaking down and just doing the multiplications explicitly by myself like you suggested. However I didn't create any fancy procedures like you did. So, there are practically no built-in Maple procedures for using commutator/anitcommutator relations on matrix data types in Maple...? I'm also surprised. Thanks again. v/r, Dan

Thanks to you both. I honestly was not trying to twist your arms to get the answer from either of you. A little ranting however, if you'll forgive me. I have a very serious pet peeve with textbooks and the "problems" that usually come at the end of chapters. Most of the time there are no examples similar to the problems given, and a lot of the time it seems like the necessary information for some problems wouldbe outright not included in the chapter or even the entire text itself ! The primary purpose of a so-called text in my humble opinion should be to TEACH, not to frustrate well some of the well meaning students who want to develop some level of proficiency or mastery in the subject. Sometimes I wonder if some authors genuinely wrote their texts to help with the teaching of the subject, or for other purposes (financial, some narcisism,etc). Ok, I'll stop now. Thanks for letting me let off my rantings somewhere. Thanks for the help also. respectfully,

Thanks to you both. I honestly was not trying to twist your arms to get the answer from either of you. A little ranting however, if you'll forgive me. I have a very serious pet peeve with textbooks and the "problems" that usually come at the end of chapters. Most of the time there are no examples similar to the problems given, and a lot of the time it seems like the necessary information for some problems wouldbe outright not included in the chapter or even the entire text itself ! The primary purpose of a so-called text in my humble opinion should be to TEACH, not to frustrate well some of the well meaning students who want to develop some level of proficiency or mastery in the subject. Sometimes I wonder if some authors genuinely wrote their texts to help with the teaching of the subject, or for other purposes (financial, some narcisism,etc). Ok, I'll stop now. Thanks for letting me let off my rantings somewhere. Thanks for the help also. respectfully,

Does the determinant of the product of two square matrices with the same determinant leave the determinant of both matrices the same ?

Does the determinant of the product of two square matrices with the same determinant leave the determinant of both matrices the same ?

Thanks, I think I sort of understand now. Since U is a function of matrices, the inverse notation `U^(-1)` returns actual inverted, (reciprocal) values, of the original function of matrices. However, if U was just an actual matrix the inverse notation `U^(-1)` would not just be the reciprocal of its elements, as there is a specific procedure for inverting a matrix. If I'm wrong in any way please don't hesitate to correct. Thanks again, v/r,

Thanks, I think I sort of understand now. Since U is a function of matrices, the inverse notation `U^(-1)` returns actual inverted, (reciprocal) values, of the original function of matrices. However, if U was just an actual matrix the inverse notation `U^(-1)` would not just be the reciprocal of its elements, as there is a specific procedure for inverting a matrix. If I'm wrong in any way please don't hesitate to correct. Thanks again, v/r,

John, Thanks, I thought that might be the way to go for part a, but I was a little hesitant. My confusion was on the term inverse. I thought that since the matrix U was defined as the natural exponential, then it's inverse may have supposed to have been the natural logarithm. i.e. The inverse of U = ln(i*a*H). I guess functions of matrices are not exactly the same as functions of real variables. (The minus one superscript at first glance is what created that confusion). Thanks, How did you get to input that 2-D math output in your post ? v/r,

John, Thanks, I thought that might be the way to go for part a, but I was a little hesitant. My confusion was on the term inverse. I thought that since the matrix U was defined as the natural exponential, then it's inverse may have supposed to have been the natural logarithm. i.e. The inverse of U = ln(i*a*H). I guess functions of matrices are not exactly the same as functions of real variables. (The minus one superscript at first glance is what created that confusion). Thanks, How did you get to input that 2-D math output in your post ? v/r,

Is the color blue already used for mapleprimes rankings ?

Here's one attempt to clarify what I mean. Take the special case of two or three dimensional vectors. Geometrically (Pictorially), they can be arrows with the length (magnitude) proportional to the magnitude of the quantity, and be pointing in the direction of whatever physical situation they may be representing, i.e. displacement. Not so simple for higher rank tensors. What would the geometrical construction for an array of elements look like in some sort of space ? A vector can be a column matrix or drawn as an arrow. A tensor ? (Just an array of elements ?) Maybe I'm now getting into fluffy philosophical stuff. Now about the more important stuff - The caramel and coffee. I originally meant the caramel melted inside the coffee, but didn't consider the issue of properly dissolving like you mentioned. That was a good catch. Dan

Here's one attempt to clarify what I mean. Take the special case of two or three dimensional vectors. Geometrically (Pictorially), they can be arrows with the length (magnitude) proportional to the magnitude of the quantity, and be pointing in the direction of whatever physical situation they may be representing, i.e. displacement. Not so simple for higher rank tensors. What would the geometrical construction for an array of elements look like in some sort of space ? A vector can be a column matrix or drawn as an arrow. A tensor ? (Just an array of elements ?) Maybe I'm now getting into fluffy philosophical stuff. Now about the more important stuff - The caramel and coffee. I originally meant the caramel melted inside the coffee, but didn't consider the issue of properly dissolving like you mentioned. That was a good catch. Dan

Thanks, to all for taking an interest in my struggles with the wealth of knowledge and resources. I did my undergrad in Physics, so I'm biased towards their side. After the continuous drilling I now believe that for my subject area, mathematics is just a tool, and I leave the rigour, and beauty/elegance to the mathematicians. Don't get me wrong, I admire and envy pure mathematicians for those same reasons (abstractness, beauty, rigor...), but unfortunately my training in physics had no time for much of that. Other than the overly simplified example of arrays of elements, is there some sort of mechanical way of picturing a tensor ? Am I stuck with the just the algebraic descriptions of tensors ? respectfully, John,I also just had the idea of incorporating caramel in some way with coffee. Does anyone know if that has already been done, or if it sounds like a good idea ? Sorry for the last off topic questions. :)