예제: 왼쪽 및 오른쪽 고유 벡터 구하기

함수 > 벡터 및 행렬 > 배열 특성 > 예제: 왼쪽 및 오른쪽 고유 벡터 구하기

부울 비교를 수행할 때 논리적 불일치를 피하려면 계산 옵션 드롭다운 목록에서 근사 등호를 활성화합니다.

1. 정방 실수 행렬을 정의합니다.

2. 고유값의 기본 정의를 사용하여 행렬 A의 람다를 구합니다.

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  <math resultRef="26">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <absval />
        <apply>
          <minus />
          <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id>
          <apply>
            <mult />
            <id xml:space="preserve">λ</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">I</id>
          </apply>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">factor</id>
      </command>
      <symResult>
        <apply>
          <mult />
          <parens>
            <apply>
              <minus />
              <id labels="VARIABLE" xml:space="preserve">λ</id>
              <real>4</real>
            </apply>
          </parens>
          <parens>
            <apply>
              <plus />
              <id labels="VARIABLE" xml:space="preserve">λ</id>
              <real>3</real>
            </apply>
          </parens>
        </apply>
      </symResult>
    </symEval>
    <formattingOverride BackgroundColor="#00FFFFFF" />
  </math>
</region>

3. eigenvals 함수를 사용하여 행렬 A의 람다를 구할 수도 있습니다.

오른쪽 고유 벡터 구하기

1. eigenvecs 함수를 사용하여 행렬 A의 오른쪽(기본값) 고유 벡터를 구합니다.

2. A x Rn~λn x Rn 사이의 편차를 확인합니다.

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<region id="ID0EMSPFB" actualWidth="130.96666666666664" actualHeight="44.2" top="979.20000000000016" left="0" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="36"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <mult /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">R<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>	<region id="ID0E2SPFB" actualWidth="134" actualHeight="44.2" top="979.20000000000016" left="172.8" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="37"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <mult /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">λ<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">R<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>	<region id="ID0ELTPFB" actualWidth="146.17666666666668" actualHeight="44.2" top="979.20000000000016" left="345.6" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="38"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <minus /> <apply> <mult /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">A</id> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">R<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </apply> <apply> <mult /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">λ<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">R<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">1</Subscript></Span> </id> </apply> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> </math> </region>

편차는 0입니다.

왼쪽 고유 벡터 구하기

1. eigenvecs 함수를 사용하여 행렬 A의 왼쪽 고유 벡터를 구합니다.

2. LnT x A~λn x LnT 사이의 편차를 확인합니다.

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편차는 0입니다.