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I am teaching a differential equations course. I allow my students to use a non-graphing calculator in exams.

I just realized that I do not know of *any* current non-graphing calculator that can handle complex matrices (in particular, finding complex eigenvectors of real matrices: if a complex eigenvalue is known, the eigenvector(s) can be found via row operations). I find this state of affairs amazing, given that the HP 15C could do this over 30 years ago, even with its meek 1-line segmented LCD display. Sadly, not even the 34S seems to include the 15C's functions to handle complex matrices via real matrices (I beg to be corrected on this!).

I (and my students) will appreciate any info on this topic.

SN
Well I'm not having much luck so far finding a non-graphing calculator that can handle complex matrix operations. I looked at the current Casio, Sharp, HP and TI models without luck. I had hoped the very capable TI36X Pro might pull another rabbit out of its hat, but no joy. It handles complex numbers and does matrix operations, but not both together.
Perhaps a program could be written for the HP 35s to do this?
The re-todayed versions of the HP15C (LE) does handle complex matrices. But at the name says, it was a limited edition a bit more complicated to find. To be fair I think the Prime does a better job because it is a graphic.
(04-27-2014 02:02 AM)Steve Simpkin Wrote: [ -> ]Perhaps a program could be written for the HP 35s to do this?

Writing a matrix program for an RPN programmable such as the 35s or 34s would be fun. Perhaps I'll write one myself. I'm still shocked by your confirmation that non-graphing calculators seem not to even be up to the abilities of the 15c, thirty years later, in this regard. (Plus, using a programmable is beyond the ability of most students in my course. They're happy enough with their sub-$20 Casio, Sharp or TI's, or else with their$100-plus graphing beasts that they cannot use in exams.)

SN
(04-26-2014 11:53 PM)supernumero Wrote: [ -> ]I am teaching a differential equations course. I allow my students to use a non-graphing calculator in exams.

I just realized that I do not know of *any* current non-graphing calculator that can handle complex matrices (in particular, finding complex eigenvectors of real matrices: if a complex eigenvalue is known, the eigenvector(s) can be found via row operations). I find this state of affairs amazing, given that the HP 15C could do this over 30 years ago, even with its meek 1-line segmented LCD display. Sadly, not even the 34S seems to include the 15C's functions to handle complex matrices via real matrices (I beg to be corrected on this!).

I (and my students) will appreciate any info on this topic.

SN

You're right, graphing there are a few, but non-graphing... it ain't any . Just the 15C and the 42S. The TI 68 has comprehensive complex support but no matrices. Neither had the Casio FX 580, although it had slightly better than usual complex for a Casio scientific.

May I suggest that you make your students do it by hand? It's quite easy, maybe tedious but also very instructive. You'd be amazed at the things they have trouble with.

And if you're lucky and they have no trouble with the chores, using a non-CAS graphing one capable of this should be tolerated IMHO.
(04-26-2014 11:53 PM)supernumero Wrote: [ -> ]in particular, finding complex eigenvectors of real matrices
How would you do that with the HP-15C?

Just curious
Thomas
(04-27-2014 02:26 AM)Tugdual Wrote: [ -> ]The re-todayed versions of the HP15C (LE) does handle complex matrices. But at the name says, it was a limited edition a bit more complicated to find.

The original 15C had exactly the same functions (including handling complex matrices). The 15C LE is now a discontinued product that, even when manufactured, carried a premium price ($100 USD) while a beastly 50G can be had for well under that amount nowadays... My point is that due to reasons that have nothing to do with lack of a sufficiently large display, of memory, or of processing power, we are stuck with (otherwise remarkable) hardware costing under$20 that is artificially crippled by limited software. I have praise for the hardware of current Casio, TI and even Canon and Sharp calculators, but they fall incredibly short on software. Even the TI 36X Pro, which is *almost* bearable, limits complex arithmetic to a few operations, and excludes complex numbers from matrices, which it limits to size 3x3 anyway. Quite absurd!

SN

PS: The HP 300s+, which I bought recently, is but a rebadged Casio sold at a premium and with worse keyboard. If only it had better software... Unfortunately, it seems that the same team of 3 Kinpo (?) employees writes the software for *every* sub-$50 calculator in the world, regardless of manufacturer. I was, in fact, rather surprised to learn that current Sharp calculators have an "LN" bug *not* present in cheap calculators from other manufacturers. It has to do with memory and costs. You can't make now a scientific capable to do that, plus what they already do and sell it for 20$. Maybe you could after a fair amount of investment, but it makes no sense: these are retail prices and you see heavy discounts, imagine the margins.

Matrix operations are already limited by memory, complex makes it double (at least). You essentially want a graphing calculator that can't graph. There is no real market for that.

Even with Moore's law and cheap labour there's a limited number of miracles that you can perform for 20$(04-27-2014 03:19 AM)Thomas Klemm Wrote: [ -> ] (04-26-2014 11:53 PM)supernumero Wrote: [ -> ]in particular, finding complex eigenvectors of real matrices How would you do that with the HP-15C? Good question. I did not mean to say I had used the 15C for this purpose; I was merely referring to the fact that the 15C supported complex matrices, and it is necessary to deal with complex matrices to find complex eigenvectors (even of real matrices). (I'm assuming the eigenvalues have already been found by some method---think of a 3x3 matrix whose real eigenvalue can be SOLVEd for, leading to a quadratic for the remaining pair of possibly complex eigenvalues. There would still remain the problem of finding the complex eigenvectors.) The 15C's support of complex matrices was limited, and *clumsy*. For the purpose of finding complex eigenvectors the most useful operation, that of taking a matrix to reduced echelon form (or, at the very least, the ability to perform row operations: subtract X times row A from row B so a user or a program could do this step-by-step) was, unfortunately, missing from the 15C. Surely one could write a program to carry out these row operations using the 15C's complex arithmetic, but the memory was so limited---perhaps someone patient enough could carry out this plan in one of the Swiss 15C clones with extended memory. I am almost feeling up to the challenge to do this for the 34S. Extending (real) M+x to become (CPLX)M+x is key for the task you asked about, and is something the 15C missed... SN (04-27-2014 03:55 AM)Manolo Sobrino Wrote: [ -> ]Matrix operations are already limited by memory, complex makes it double (at least). You essentially want a graphing calculator that can't graph. There is no real market for that. Okay, I concede that memory may be a limitation (what the 34S couldn't do with just a little extra memory!!!). Still, there are sub-$20 calculators that can handle 4x4 real matrices (Canon f-789sga comes to mind---in fact this one's price dropped to sub-$10 at some point), so they have at least as much memory as needed to handle 4x2, and probably 3x3 complex matrices, which would be quite useful---and has nothing to do with asking for the ability to *graph*. Then again, if students didn't use calculators to cheat I'd have no problem letting them use a 50g, which would be the best sub-$90 purchase of their life.

SN
(04-27-2014 04:10 AM)supernumero Wrote: [ -> ]I concede that memory may be a limitation (what the 34S couldn't do with just a little extra memory!!!).

That's a textbook example for using the irrealis. Maybe nice for your students, too.

Seriously, the WP 34S isn't limited by memory alone but also (and mainly) by lacking data types. HP-42S matrix handling runs circles around the HP-15C, BTW.

d:-)
(04-27-2014 05:46 AM)walter b Wrote: [ -> ]Seriously, the WP 34S isn't limited by memory alone but also (and mainly) by lacking data types.

(03-19-2014 08:57 AM)Paul Dale Wrote: [ -> ]There wasn't enough RAM to include a type along with each register.

It appears the lack of data types is caused by the limitation of memory.
Are there other reasons?

Cheers
Thomas
(04-27-2014 07:24 AM)Thomas Klemm Wrote: [ -> ]
(04-27-2014 05:46 AM)walter b Wrote: [ -> ]Seriously, the WP 34S isn't limited by memory alone but also (and mainly) by lacking data types.

(03-19-2014 08:57 AM)Paul Dale Wrote: [ -> ]There wasn't enough RAM to include a type along with each register.

It appears the lack of data types is caused by the limitation of memory.

Well, almost everything is caused by lack of memory - be it silicon or biological matter.
According to the user's guide, it handles up to 6 matrices with 10 by 10 in size.
However it doesn't mention what data types are supported in matrix operations.
I wonder if someone having one of these beauties can check it out?
(04-27-2014 12:49 PM)jebem Wrote: [ -> ]What about the Casio FX-5800P?
According to the user's guide, it handles up to 6 matrices with 10 by 10 in size.
However it doesn't mention what data types are supported in matrix operations.
I wonder if someone having one of these beauties can check it out?

The Casio fx-9860g series handles complex matrices (I just tested it out). Although these are graphics calculators I'm pretty sure that the functions and most of the programing functions are identical on the Casio fx-5800p.
(04-27-2014 05:36 AM)Manolo Sobrino Wrote: [ -> ]
(04-27-2014 03:59 AM)supernumero Wrote: [ -> ]Good question. I did not mean to say I had used the 15C for this purpose; I was merely referring to the fact that the 15C supported complex matrices, and it is necessary to deal with complex matrices to find complex eigenvectors (even of real matrices). (I'm assuming the eigenvalues have already been found by some method---think of a 3x3 matrix whose real eigenvalue can be SOLVEd for, leading to a quadratic for the remaining pair of possibly complex eigenvalues. There would still remain the problem of finding the complex eigenvectors.)
... and you never worked out the algebra of how doing this with 2 systems of linear equations and just real numbers, just in case you want to use a cheap calculator, that in any case can't help you with the homogeneous system. I don't think that you or your students really need a calculator.

The proximate reason I started this thread was solving an exercise straight from Boyce-DiPrima's book to present in a lecture:

Find the general solution to the system:
$$x'_1 = -3x_1 + 2x'_3$$
$$x'_2 = x'_1-x'_2$$
$$x'_3 = -2x'_1-x'_2$$

or $$\mathbf{x}' = A\mathbf{x}$$ in matrix-vector notation.

The characteristic values of $$A$$ are $$\lambda = -2, -1\pm\sqrt2i.$$ The eigenvectors are obtained by solving the singular homogeneous linear 3x3 systems $$(A-\lambda I)\xi = \mathbf{0},$$ which is a simple enough task but (even in the real case) is beyond the functionality cheap calculators (entirely for non-intrinsic reasons such as hardware limitations). I did the calculations by hand: They are, of course, completely routine, but it's quite easy to make mistakes.

SN
(04-27-2014 01:26 PM)Katie Wasserman Wrote: [ -> ]The Casio fx-9860g series handles complex matrices (I just tested it out). Although these are graphics calculators I'm pretty sure that the functions and most of the programing functions are identical on the Casio fx-5800p.

I have an fx-5800P. Sadly, complex number entry is disabled in the matrix editor.

I appreciate the replies. It is clear that few calculators give complex numbers the "full citizen" treatment, and none of them are non-graphing.

Le plus court chemin entre deux vérités dans le domaine réel passe par le domaine complexe.--Jacques Hadamard
One more vote in the ballot box for the 42S. And another pair of votes for the 15C & 15C-LE.

I hope you can find one (or all three) of those.
(04-27-2014 02:02 AM)Steve Simpkin Wrote: [ -> ]Well I'm not having much luck so far finding a non-graphing calculator that can handle complex matrix operations. I looked at the current Casio, Sharp, HP and TI models without luck. I had hoped the very capable TI36X Pro might pull another rabbit out of its hat, but no joy. It handles complex numbers and does matrix operations, but not both together.
Perhaps a program could be written for the HP 35s to do this?

The 36 can, especially in classic entry mode, solve d/dx (f(x)=0. Unlike the Casio,Sharp,HP 35s, and even WP 34S (which is easily a more capable platform)...can do cross product in addition to dot products of a 3D vector.
(04-27-2014 05:44 PM)supernumero Wrote: [ -> ]
(04-27-2014 01:26 PM)Katie Wasserman Wrote: [ -> ]The Casio fx-9860g series handles complex matrices (I just tested it out). Although these are graphics calculators I'm pretty sure that the functions and most of the programing functions are identical on the Casio fx-5800p.

I have an fx-5800P. Sadly, complex number entry is disabled in the matrix editor.

I appreciate the replies. It is clear that few calculators give complex numbers the "full citizen" treatment, and none of them are non-graphing.

Le plus court chemin entre deux vérités dans le domaine réel passe par le domaine complexe.--Jacques Hadamard

The latest CASIO FD10 Pro also supports complex matrices since it has a similar OS of the 9860 series. And it has a similar large screen. And it is advertised a programmable calculator which has graph function.

So what is a graphic calculator? In theory, a programmable calculator having a LCD screen can be programmed to draw functions, such as 42S and 5800p. Here the border between graphic and non-graphic calculators becomes ambiguous. Now consider those exams require "calculators without memory function". Even the cheap scientific calculator has several variables to store numerical answers. And an adding machine can also has the "M+" function.
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