/sci/ - Science & Math » Thread #11034847

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Anonymous Sat 05 Oct 21:33:01 2019 No.11034847 View Reply Original Report

Quoted By: >>11034884 >>11034945 >>11034952 >>11034953 >>11035967 >>11037488 >>11037896 >>11038306

Is a 1x1 matrix the same as a scalar?

Anonymous

Anonymous Sat 05 Oct 2019 21:35:01 No.11034851 Report

Quoted By: >>11037545

a whole thread? really?

Anonymous

Anonymous Sat 05 Oct 2019 21:47:46 No.11034884 Report

Quoted By:

>>11034847
no

Anonymous

Anonymous Sat 05 Oct 2019 22:12:13 No.11034945 Report

Quoted By: >>11034957

>>11034847
technically a scalar is a 1x1 matrix, but no one cares and there is no reason too

Anonymous

Anonymous Sat 05 Oct 2019 22:13:49 No.11034952 Report

Quoted By:

>>11034847
no such thing as "the same" nor such thing as "difference". The world is just one big anal extension of the monad. Perpetually leaking metaphysical turd

Anonymous

Anonymous Sat 05 Oct 2019 22:14:21 No.11034953 Report

Quoted By:

>>11034847
Not because it's still a single element vector. It's like asking if a set with a single element is just the element itself.

Anonymous

Anonymous Sat 05 Oct 2019 22:15:45 No.11034957 Report

Quoted By: >>11034967 >>11035997 >>11036111 >>11037482 >>11039867

>>11034945
But you can't multiply a 2x3 matrix by a 1x1 matrix. You can multiply by a scalar.

Anonymous

Anonymous Sat 05 Oct 2019 22:21:22 No.11034967 Report

Quoted By: >>11036101

>>11034957
whats the difference between a 1x1 matrix and a scalar
>But you can't multiply a 2x3 matrix by a 1x1 matrix. You can multiply by a scalar.
both terms are equivalent. multiplication rules between matrices apply but its a special case for 1x1 matrix

Anonymous

Anonymous Sun 06 Oct 2019 06:06:01 No.11035967 Report

Quoted By: >>11036069 >>11037474

>>11034847
A scalar is a zeroth-order tensor, what you're calling a matrix is a second-order tensor.

Just because it's possible to treat a 1x1 matrix as a scalar doesn't make it one.

Anonymous

Anonymous Sun 06 Oct 2019 06:22:49 No.11035997 Report

Quoted By:

>>11034957
THIS. End of discussion.

Anonymous

Anonymous Sun 06 Oct 2019 06:39:42 No.11036022 Report

Quoted By:

Too much MATLAB mate... Too much MATLAB

Anonymous

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Anonymous Sun 06 Oct 2019 07:00:00 No.11036069 Report

Quoted By:

>>11035967
So-called "scalar multiplication" is just a special case of tensor product. Believe me, it's much more beautiful this way

Anonymous

Anonymous Sun 06 Oct 2019 07:14:16 No.11036101 Report

Quoted By:

>>11034967
>whats the difference between a 1x1 matrix and a scalar
intent

Anonymous

Anonymous Sun 06 Oct 2019 07:19:33 No.11036111 Report

Quoted By:

>>11034957
they are different operations, they are not the same product, so no contradiction

Anonymous

Anonymous Sun 06 Oct 2019 20:02:55 No.11037474 Report

Quoted By:

>>11035967
wrong. Matrices have no associated transformation rules under change of coordinates

Anonymous

Anonymous Sun 06 Oct 2019 20:06:15 No.11037482 Report

Quoted By:

>>11034957
multiplication != multiplication. They're just called the same thing, but they're not the same operation

Anonymous

Anonymous Sun 06 Oct 2019 20:09:35 No.11037488 Report

Quoted By: >>11037489 >>11037508

>>11034847
better question is, is complex number the same as 1xm matrix?

Anonymous

Anonymous Sun 06 Oct 2019 20:10:06 No.11037489 Report

Quoted By:

>>11037488
1x2

Anonymous

Anonymous Sun 06 Oct 2019 20:14:47 No.11037508 Report

Quoted By:

>>11037488
2x2 of the format
a -b
b a
for real a,b
this under matrix addition/matrix multiplication can easily be put in an isomorphism with complex under addition/multiplication respectively

Anonymous

Anonymous Sun 06 Oct 2019 20:25:10 No.11037545 Report

Quoted By:

>>11034851

a whole matrix for a single scalar? really?

Anonymous

Anonymous Sun 06 Oct 2019 23:04:42 No.11037896 Report

Quoted By: >>11038085

>>11034847
Literally all a matrix is is an array of entries. The operations and mathematical properties of a matrix depends entirely on what the matrices are being used to represent (linear transformation, coordinate transformation, tensor, system of equations, table of data, operator, etc. etc.)

Anonymous

Anonymous Mon 07 Oct 2019 01:00:53 No.11038082 Report

Quoted By:

Well, scalar multiplication is a linear transformation and its associated matrix is the scalar itself. So maybe.

????_Solivagus (Polynomial Philosopher)

????_Solivagus (Polynomial Philosopher) Mon 07 Oct 2019 01:05:03 No.11038085 Report

Quoted By:

>>11037896
So a matrix is an array of variables you say?

English, portrayed.

~The P00rly Paid P0et

Anonymous

Anonymous Mon 07 Oct 2019 02:55:58 No.11038306 Report

Quoted By:

>>11034847
There is a natural isomorphism between the space of 1x1 matrices over R and R. So, by the perspective of Linear Algebra, they are essentially the same

Anonymous

Anonymous Mon 07 Oct 2019 18:39:01 No.11039867 Report

Quoted By:

>>11034957
lol

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