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/sci/ - Science & Math

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7036116 No.7036116 [Reply] [Original]

Is a matrix containing only zeros equal to the real number 0?

>> No.7036118

if you define the matrix to be vectors on any standard coordinate system then a vector of length 0 @ 0,0,0... would be just 0.

>> No.7036122

>>7036116
No.

>> No.7036128

yes and it is also equal to the number of times you get laid

>> No.7036130

No, becouse equal matrices have same dimension. But you can mark them both with 0.

>> No.7036133

>>7036116
>Is matrix equal number?

What a terrible question. How can two mathematical objects which are distinct, equal one another. A matrix of zeros, being the zero matrix, can hold the same properties and identities as zero, but both objects fundamentally exist on different topologies and thus cannot be compared.

>> No.7036134

>>7036133
If two different mathematical objects have the exact same properties, they are equal.

>> No.7036143

>>7036134
No they're not. That's not how math works. They exist on different topologies as I just said. They both serve the same function in their respective topologies, but they themselves are not equal.

Let's relate this to sports. In this case the topology will be the sport. We'll pick basketball and baseball. In both cases you need a ball (just as both topologies need a zero element). For baseball it is of course the baseball and for basketball it is of course the basketball. Both balls have similar properties and serve similar purposes for the game (i.e. they are thrown around and handled by the players, used to score points, spherical etc. I admit its not a perfect analogy). However, just because both balls (mathematical objects), which exist in different sports (topologies) serve the same/similar purpose and have similar properties, it doesn't mean baseball = basketball.

>> No.7036148
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7036148

>>7036143
> topologies need a zero element

You went more full retard than the OP. Please learn the difference between a topology and an algebraic structure.

>> No.7036157

>>7036143
But if both balls share the exact same properties: elasticity, size, shape, smell, sound, handling, etc. they could be interchanged between the sports and no one would be able to tell the difference.

The only difference between different topologies is that the objects are different and interact in different ways.

>> No.7036158

>>7036148
Alright sure, you got me. I was being careless. They are really groups, but even still a group is based off a topology.

>> No.7036161

>>7036157
But that's the point of the analogy. They don't share exactly the same properties and neither does the zero element matrix and the number zero.

>> No.7036162

>>7036161
What properties don't they share?

>> No.7036172

>>7036162
Well for one they're inherently different structures. One is an array of numbers, one is a single number. But aside from that their groups are different. For example, matrix groups don't have the commutative rule. That is, for two matrices A and B, AB != BA but for two numbers ab it is true that ab = ba.

>> No.7036192
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7036192

>>7036172
Can someone please ban this retard before he spreads more misinformation?

>For example, matrix groups don't have the commutative rule.
A + B = B + A
holds for all matrices

>That is, for two matrices A and B, AB != BA
Matrices are not a group with respect to multiplication. Not every matrix is invertible.

>> No.7036193

>>7036172
I know that a matrix is not the same as a real number. What I'm saying is that the zero matrix has the same properties as the real number zero. That is, for example if Z is the zero matrix, then ZA = AZ = 0*A = A*0. And so on for every property.

>> No.7036212

>>7036162
being a (real) number
being a matrix

>> No.7036218

>>7036192
>commutative rule
>asserts A + B = B + A
epiiiiiiiiic

>> No.7036223

You can identify them. The more important question is: What information do you gain from doing so? Why would you do it?

>> No.7036226

>>7036218
Are you saying matrices are not a commutative group with respect to addition?

>> No.7036235 [DELETED] 

>>7036226
I'm saying you're confused
http://en.wikipedia.org/wiki/Commutative_property

>> No.7036238

>>7036172
>>7036218

Please mods, ban those retards. We're talking about 0, which is the neutral element for SUMMATION, not for MULTIPLICATION, so the commutative rule that >>7036192 stated is actually correct.
Stop being ignorant, study moar.

>> No.7036239

>>7036212
This is a conclusion, not a property.

>> No.7036241

No, a matrix is not a number.

>> No.7036244

>>7036235
as just stated before, a complete idiot sir.

Binary operation means also summation, dense idiot.

>> No.7036247

>>7036235
Addition of matrices is a binary operation and is commutative. What is your problem, retard?

>> No.7036250

>>7036241
That wasn't the question. The question was if a matrix with an arbitrary number of elements who are all zero is equal to the real number 0.

I redefined the question (I'm not OP, btw) here:
>>7036134
to be "Does a matrix with an arbitrary number of elements who are all zero share all properties with the real number 0?"

>> No.7036254
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7036254

>>7036128
ayyyy

>> No.7036256

>>7036250
>Does a matrix with an arbitrary number of elements who are all zero share all properties with the real number 0?

The additive neutral elements of all rings share the same algebraic properties. What a deep insight for a 12 year old ...

>> No.7036259

>>7036239
a conclusion of what? what's a property then?
Normally in math one formalizes 'properties' in terms of sets. And the real number 0 is an element of R, while no zero matrix is an element of R.

>> No.7036261

>>7036256
How was your day today?

>> No.7036280

>>7036250
what's the space that's closed for multiplication?
Also division isn't defined.

>> No.7036284

>>7036256
hehehehehe

>> No.7036286

>>7036280
>what's the space that's closed for multiplication?
The space of all matrices.

>Also division isn't defined.
No shit. You cannot divide by zero.

>> No.7036293

>>7036286
What's 0/1?
what's
[5 0]
[0 5]
multiplied by
[0 0 0]
[0 0 0]
[0 0 0]
?

>> No.7036295

>>7036293
Both are 0. Please do your homework alone.

>> No.7036300

>>7036295
you are using a different definition of matrix multiplication than me.
Can you please provide the construction?

>> No.7036308

>>7036300
>you are using a different definition of matrix multiplication than me.

Which definition are you using?

>> No.7036319

>>7036116
they are not equal they are congruent.

>> No.7036337

>>7036308
this one
http://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product_.28two_matrices.29
If OP further reduces his criteria to "Does a square zero matrix share all properties with the real number 0?"
I think the algebraic properties would be satisfied.

But the order and completeness properties aren't.

>> No.7037650

>>7036134
An object can only be equal to itself in math. E.g: 5+5,9+1,10 are equal to themselves and each other because they are the same thing. Assuming that they all lie on the same axis. However a point on the x axis and a point on the y axis is not necessarily the same even if they have the same value. Eg (5,5). They are equal value in their respective dimensions. However the keyword you (OP) may be looking for I believe is "isomorphic".

>> No.7037660

>>7037650
What's the difference between isomorphic and homeomorphic?

>> No.7037682

>>7036295
How do you multiply a 2x2 matrix by a 3x3 matrix? A*B is only possible if columns(A) = rows(B)

>> No.7037821

>Ctrl+f "linear"
>no mention of linear algebra

Wow guys, this is a simple math question.

>> No.7037825

>>7036116
You can't say they are equal, but depending on the mathematical context they might be isomorphic. For example if we define some set like
<div class="math">\mathbf{A} = \left\{x\cdot \mathbf{1}_{n\times n}: x \in \mathbf{R}\right\}</div>
then
<div class="math">\mathbf{A} \simeq \mathbf{R}</div>
and thus
<div class="math">\mathbf{0}_{n\times n} \simeq 0</div>
here.

>> No.7037834

>>7037682
You can embed them into higher dimensional matrices by adding rows and columns of zeros.

>> No.7037838

A matrix is not equal to a number.

The determinant of a matrix of zeroes is equal to the number zero.

>> No.7037840

>>7037825
your fancy notation is lost on OP, anon..

>> No.7037845

>>7037825
By that reasoning you'd also have to say 0.999... and 1 are not equal but only "isomorphic".

>> No.7037853

>>7037845
No they are equal, as they describe both exactly the same mathematical object, as
<div class="math">0.\overline{9} = \sum_{k=1}^\infty 9\cdot 10^{-k} = 9 \sum_{k=1}^\infty \left( \frac{1}{10} \right)^k = \frac{9}{1-\frac{1}{10}} - 9 = 1\,.</div>

>> No.7037862

>>7037853
They cannot be equal, only isomorphic. They live in different sets. 0.999... is an element of the decimal numbers while 1 is an element of the real numbers defined abstractly as a field.

>> No.7037866

>>7037862
The decimal numbers are a subset of the reals.

>> No.7037870

>>7037866
No, but they are isomorphic to a subset of the reals.

>> No.7037882

>>7037870
The real number 0.999... and the real number 1.000... are equal, because they are the same real number.

>> No.7037917

>>7036116
Is a parking lot of black cars equal to a black car?

Checkmate, atheists

>> No.7037927

>>7036133
>exist on different topologies and thus cannot be compared

This is an awesome /sci/ troll! I'll have to use it next time.

>> No.7037930

>>7037882
The real numbers are an abstractly defined field and not synonymous with the set of decimal numbers. They are only isomorphic.

>> No.7037936

>ask simple question albeit retarded
>devolves into .999 = 1 thread

Good work /sci/. For OP, the answer is no: the real number 0 is in R, while the zero matrix in n dimensions lives in R^{n^2}.

>> No.7038213

OP absolutely not, do you even math?

>> No.7038240

Yes, they can be equal.

>> No.7038286

0 is indeed a matrix living in R exp 1x1