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Antti H S Laaksonen 2017-02-18 16:33:08 +02:00
parent bbd1df2901
commit 62ae348501
1 changed files with 3 additions and 3 deletions
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luku23.tex
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@ -182,7 +182,7 @@ For example,
Matrix multiplication is associative, Matrix multiplication is associative,
so $A(BC)=(AB)C$ holds, so $A(BC)=(AB)C$ holds,
but it is not commutative, but it is not commutative,
so $AB = BA$ does not hold. so $AB = BA$ does not usually hold.
\index{identity matrix} \index{identity matrix}
@ -534,7 +534,7 @@ X^n \cdot
1 \\ 1 \\
\end{bmatrix}. \end{bmatrix}.
\] \]
The power $X^n$ can be calculated in The value of $X^n$ can be calculated in
$O(k^3 \log n)$ time, $O(k^3 \log n)$ time,
so the value of $f(n)$ can also be calculated so the value of $f(n)$ can also be calculated
in $O(k^3 \log n)$ time. in $O(k^3 \log n)$ time.
@ -576,7 +576,7 @@ X =
In the first $k-1$ rows, each element is 0 In the first $k-1$ rows, each element is 0
except that one element is 1. except that one element is 1.
These rows replace $f(i)$ with $f(i+1)$, These rows replace $f(i)$ with $f(i+1)$,
$f(i+1)$ with $f(i+2)$, etc. $f(i+1)$ with $f(i+2)$, and so on.
The last row contains the coefficients of the recurrence The last row contains the coefficients of the recurrence
to calculate the new value $f(i+k)$. to calculate the new value $f(i+k)$.