Examples of using A transpose in English and their translations into Polish
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Colloquial
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Official
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Medicine
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Ecclesiastic
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Ecclesiastic
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Official/political
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Programming
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Computer
That's A transpose.
It's going to be equal to A transpose.
The null space of A transpose, we saw already, that's the orthogonal complement of V.
We're just taking A times A transpose.
So it's just equal to A times A transpose, times x, which is a huge simplification.
People also translate
I need to multiply that times A transpose.
And what is it A transpose equal to?
Which is the same thing as the nullspace of A transposed.
So it's just A times Ik, times A transpose-- I always forget that second A transpose right there-- times x.
Which is the same thing as the column space of A transposed.
The module offers a transpose switch with 3 positions, allowing you totranspose the notes up or down by 1 octave.
The row space of A is the column space of A transpose.
So A transpose A inverse becomes the inverse of the k by k identity matrix, which is just the k by k identity matrix.
If they're all orthonormal,then this is the same thing as a transpose.
In the last video,I showed you that the rank of A transpose is the same thing is the rank of A. .
That right there is the row space of A which is the same thing as a column space of A transpose.
But that simply, if we assume an orthonormal basis,then A transpose A becomes the k by k identity matrix.
We know that the rank of A transpose plus the nullity of A transpose is equal to the number of columns of A transpose.
Or another way to think of it is-- sorry, not just the dimension of A transpose, the dimension of the null space of.
So the dimension-- get you tongue-tied sometimes-- the dimension of the orthogonal complement of V is going to be equal do the dimension of A transpose.
Also, there is a transpose function allowing you to accurately tune instruments in other keys, such as F, B-flat and E-flat as well as C.
We could write this, just to understand the terminology, that's the left nullspace,which is the same thing as the nullspace of A transposed.
There's also a transpose function that lets you smoothly tune transposing instruments in F, Bb, and Eb as well as the conventional C scale.
And if you have a good memory, I don't use the word a lot, this thing is the nullity-- this is the nullity of A transpose.
And the projection of x onto V is just equal to A times A transpose, where A is the matrix where each of the column vectors are the basis vectors for our subspace V.
I hope you already appreciate that this is a lot less painful than we had to take A transpose A, and then inverse it in between.
The same result if you switch A and A transpose, we also learned that the orthogonal complement of the column space of A is equal to the left nullspace of A. .
And if we construct A in that way, then the projection of x onto V,this linear transformation can be represented as A times A transpose times x.
So we can rewrite this statement, right here,as the rank of A plus the nullity of A transpose is equal to n, and the rank of A is the same thing as the dimension of the column space of A. .
And then the nullity of A transpose is the same thing as the dimension of the null space of A transpose-- that's just the definition of nullity-- they're going to be equal to n.
