/sci/ - Science & Math

a whole thread? really?

>>11034847
no

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

>>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

>>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.

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

>>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

>>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.

>>11034957
THIS. End of discussion.

Too much MATLAB mate... Too much MATLAB

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

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

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

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

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

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

>>11037488
1x2

>>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

>>11034851

a whole matrix for a single scalar? really?

>>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.)

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

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

English, portrayed.

~The P00rly Paid P0et

>>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

>>11034957
lol