Examples of using Matrix multiplication in English and their translations into Polish
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So let's see, matrix multiplication.
We have learned about matrix addition,matrix subtraction, matrix multiplication.
Well think about how matrix multiplication works out.
Matrix multiplication or matrix products with vectors is always a linear transformation.
That's how we learned matrix multiplication.
And then matrix multiplication here, minus 6 times x plus 6 times y is equal to 6.
The group operation is matrix multiplication.
The way we learned matrix multiplication, we said, 3 times x, plus 2 times y is equal to 7.
And all of that is really just matrix multiplication.
Understanding matrix multiplication is just the beginning.
We once again reduced everything to just a matrix multiplication.
So let's see if matrix multiplication applies there.
And you can think about that just in terms of how we learned matrix multiplication, why that happens.
That's just traditional matrix multiplication that we learned several videos ago.
So all of these things that you're doing in your fancy 3D games on your Xbox or your Playstation, they're all just matrix multiplications.
And it's important to realize when we're doing matrix multiplication, that direction matters.
Let's do some more matrix multiplication examples, because I think it is all about seeing as many examples as possible.
I didn't divide everything by 30, just so the matrix multiplication's a little easier.
What we will see is this won't be true for every matrix operation that we study andin particular this will not be true for matrix multiplication.
My brain is starting to slow down,having to do matrix multiplications with fractions with negative numbers.
In the same paper he also presented an asymptotically fast algorithm to perform matrix inversion, based on the fast matrix multiplication algorithm.
The only way that we know to define matrix multiplication is if these middle two numbers are the same.
If these two numbers weren't equal, if the number of columns here were not equal to the number of rows here, then this would not be a valid operation,at least the way that we have defined matrix multiplication.
In this case they clearly do not equal each other, so matrix multiplication is not defined here.
It's important when we're doing matrix multiplication, to confirm that it matters what direction you do the multiplication in.
Now this right here,this problem can be rewritten just based on how we have defined matrix multiplication, et cetera, et cetera, as this.
Ordinary vector algebra uses matrix multiplication to represent linear maps, and vector addition to represent translations.
According to another basic theorem, any group in the category of affine varieties has a faithful finite-dimensional linear representation: we can consider it to be a matrix group over K,defined by polynomials over K and with matrix multiplication as the group operation.
So the way that we have defined matrix multiplication, you cannot multiply these two matrices. .
One can begin with those applying the formula of differences of squares and using the trygonometric tables and formulas[Kordos, Wykłady z historii matematyki, p. 125-126], through Gauss' method for multiplying complex numbers, up to Karacuba algorithm for multiplying large numbers andStrassen's algorithm of matrix multiplication.