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1.4 $BN9TNs$N@5CM@-!"IiCM@-(B


\begin{jdefinition} $A=(a_{ij})$ $B$r(B $n$ $B<!<BBP>N9TNs$H$9$k!#(B \begin{enumerate... ...Iff$ $A$ $B$N8GM-CM$K@5$N$b$N!


\begin{jexample} $A=\begin{pmatrix}2 & 0 0 & 3\end{pmatrix}$ $B$N$H$-!


\begin{jtheorem} $A=(a_{ij})$ $B!
($B>ZL@$N$"$i$9$8(B) $BE,Ev$J8r9TNs(B $ U$ $B$,B8:_$7$F!"(B

$\displaystyle U^T A U=\begin{pmatrix}\lambda_1 & & \bigzerou & \ddots & \\ \bigzerol & & \lambda_n\end{pmatrix}. $

$B$3$N$H$-(B $ x=U y$ $B$H$*$/$H(B ($ y=U^T x$ $B$H$*$/$H(B)$B!"(B

$\displaystyle \left(A x,x\right) = \left(A U y, U y\right) = \left(U^T A U y, y... ...nd{pmatrix}y,y\right) =\lambda_1 y_1^2+\lambda_2 y_2^2+\cdots+\lambda_n y_n^2. $

$ x=0$ $ \Iff$ $ y=0$ $B$KCm0U$9$l$PNI$$!#(B $ \qedsymbol$

ARRAY(0xf8af6c)

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Next: $B;29MJ88%(B Up: 1 $B6KCMLdBj(B Previous: 1.3 $B6KCMLdBj$NDjM}(B
Masashi Katsurada
$BJ?@.(B23$BG/(B7$B7n(B17$BF|(B