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Display information for equation id:math.1355.83 on revision:1355
* Page found: Dynamische Systeme und deterministisches Chaos (eq math.1355.83)
(force rerendering)Occurrences on the following pages:
Hash: 16a544018852222c9929c2ca4a2b63a4
TeX (original user input):
\det (A-\lambda 1)=0\Rightarrow \left| \left( \begin{matrix}
{{a}_{11}}-\lambda & {{a}_{12}} \\
{{a}_{21}} & {{a}_{22}}-\lambda \\
\end{matrix} \right) \right|=\left( {{a}_{11}}-\lambda \right)\left( {{a}_{22}}-\lambda \right)-{{a}_{12}}{{a}_{21}}={{\lambda }^{2}}-\lambda \mathbf{t}rA+\det A=0
TeX (checked):
\det(A-\lambda 1)=0\Rightarrow \left|\left({\begin{matrix}{{a}_{11}}-\lambda &{{a}_{12}}\\{{a}_{21}}&{{a}_{22}}-\lambda \\\end{matrix}}\right)\right|=\left({{a}_{11}}-\lambda \right)\left({{a}_{22}}-\lambda \right)-{{a}_{12}}{{a}_{21}}={{\lambda }^{2}}-\lambda \mathbf {t} rA+\det A=0
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MathML (2.284 KB / 448 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>det</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>A</mi><mo>−</mo><mi>λ</mi><mn>1</mn><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo>⇒</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mtable columnspacing="1em" rowspacing="4pt"><mtr><mtd><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>1</mn></mrow></mrow></msub><mo>−</mo><mi>λ</mi></mtd><mtd><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>2</mn></mrow></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mn>1</mn></mrow></mrow></msub></mtd><mtd><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mn>2</mn></mrow></mrow></msub><mo>−</mo><mi>λ</mi></mtd></mtr><mtr><mtd></mtd></mtr></mtable></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mo>=</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>1</mn></mrow></mrow></msub><mo>−</mo><mi>λ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mn>2</mn></mrow></mrow></msub><mo>−</mo><mi>λ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo>−</mo><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>2</mn></mrow></mrow></msub><msub><mi>a</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mn>1</mn></mrow></mrow></msub><mo>=</mo><msup><mi>λ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><mi>λ</mi><mrow data-mjx-texclass="ORD"><mi mathvariant="bold">t</mi></mrow><mi>r</mi><mi>A</mi><mo>+</mo><mi>det</mi><mo>⁡</mo><mi>A</mi><mo>=</mo><mn>0</mn></mstyle></mrow></math>
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