Is a square zero matrix positive semidefinite?












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Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?






linear-algebra matrices positive-semidefinite







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    1












    $begingroup$


    Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?






    linear-algebra matrices positive-semidefinite







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      1












      1








      1





      $begingroup$


      Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?






      linear-algebra matrices positive-semidefinite







      share|cite|improve this question











      $endgroup$




      Does the fact that a square zero matrix contains non-negative eigenvalues (zeros) make it proper to say it is positive semidefinite?






      linear-algebra matrices positive-semidefinite




      linear-algebra matrices positive-semidefinite






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      share|cite|improve this question













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      edited 7 hours ago







      Kay

















      asked 7 hours ago









      KayKay

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          The $n times n$ zero matrix is positive semidefinite and negative semidefinite.






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            $begingroup$

            "When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.






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              2 Answers
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              5












              $begingroup$

              The $n times n$ zero matrix is positive semidefinite and negative semidefinite.






              share|cite|improve this answer









              $endgroup$


















                5












                $begingroup$

                The $n times n$ zero matrix is positive semidefinite and negative semidefinite.






                share|cite|improve this answer









                $endgroup$
















                  5












                  5








                  5





                  $begingroup$

                  The $n times n$ zero matrix is positive semidefinite and negative semidefinite.






                  share|cite|improve this answer









                  $endgroup$



                  The $n times n$ zero matrix is positive semidefinite and negative semidefinite.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 7 hours ago









                  Gary MoonGary Moon

                  31613




                  31613























                      2












                      $begingroup$

                      "When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.






                      share|cite|improve this answer









                      $endgroup$


















                        2












                        $begingroup$

                        "When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.






                        share|cite|improve this answer









                        $endgroup$
















                          2












                          2








                          2





                          $begingroup$

                          "When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.






                          share|cite|improve this answer









                          $endgroup$



                          "When in doubt, go back to the basic definitions"! The definition of "positive semi-definite" is "all eigen-values are non-negative". The eigenvalues or the zero matrix are all 0 so, yes, the zero matrix is positive semi-definite. And, as Gary Moon said, it is also negative semi-definite.







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered 7 hours ago









                          user247327user247327

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