Jordan matrix

<p>In the <a href="/facts/Mathematics/pxTouaz4">mathematical</a> discipline of <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix theory</a>, a Jordan matrix, named after <a href="/facts/Camille_Jordan/gmLuEJ4e">Camille Jordan</a>, is a <a href="/facts/Block_matrix/fPI8HX9f">block diagonal matrix</a> over a <a href="/facts/Ring_(mathematics)/JnCUXz63">ring</a> R (whose <a href="/facts/Identity_element/9nss3xHY">identities</a> are the <a href="/facts/0_(number)/4NBRtKHc">zero</a> 0 and <a href="/facts/1_(number)/m3wpSfMf">one</a> 1), where each block along the diagonal, called a Jordan block, has the following form:

[
            
              
                
                  λ
                
                
                  1
                
                
                  0
                
                
                  ⋯
                
                
                  0
                
              
              
                
                  0
                
                
                  λ
                
                
                  1
                
                
                  ⋯
                
                
                  0
                
              
              
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋮
                
                
                  ⋱
                
                
                  ⋮
                
              
              
                
                  0
                
                
                  0
                
                
                  0
                
                
                  λ
                
                
                  1
                
              
              
                
                  0
                
                
                  0
                
                
                  0
                
                
                  0
                
                
                  λ
                
              
            
            ]
          
        
        .
      
    
    {\displaystyle {\begin{bmatrix}\lambda &1&0&\cdots &0\\0&\lambda &1&\cdots &0\\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\lambda &1\\0&0&0&0&\lambda \end{bmatrix}}.}

</p>

Jordan matrix open-in-new

Jordan matrix