{"id":723,"date":"2021-05-06T12:18:25","date_gmt":"2021-05-06T06:48:25","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=723"},"modified":"2021-10-30T07:40:44","modified_gmt":"2021-10-30T07:40:44","slug":"what-is-a-symmetric-matrix","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-a-symmetric-matrix\/","title":{"rendered":"What is a Symmetric Matrix?"},"content":{"rendered":"\n

A square matrix is said to be a symmetric matrix if for all values of i and j or we can say that  <\/p>\n\n\n\n

Example of symmetric matrix is-<\/p>\n\n\n\n

<\/p>\n\n\n\n

And if a square matrix   is called skew symmetric matrix if it follows the following conditions-<\/p>\n\n\n\n

  1. for all values of i and j. <\/li>
  2. The diagonal elements of the matrix should be zero<\/li><\/ol>\n\n\n\n

    For example- <\/p>\n\n\n\n

    <\/p>\n\n\n\n

    Note-<\/strong><\/p>\n\n\n\n

    We can express any square matrix as the sum of two matrices, where one is symmetric and the other one is anti-symmetric.<\/p>\n\n\n\n

    So that-<\/p>\n\n\n\n

    Square matrix = Symmetric matrix + Anti-symmetric matrix<\/strong><\/p>\n\n\n\n

    Important points about symmetric matrix- <\/strong><\/p>\n\n\n\n

    1. Eigen vectors of a symmetric matrix corresponding to different Eigen values are orthogonal.<\/li><\/ol>\n\n\n\n
      1. The product of two symmetric matrices A and B is symmetric if AB = BA.<\/li><\/ol>\n\n\n\n
        1. Inverse of a non-singular symmetric matrix A is symmetric.<\/li>
        2. We can reduce a real symmetric matrix A to a diagonal form N\u2019A N = D, here N is the normalized orthogonal modal matrix of A and D is called spectoral matrix.<\/li><\/ol>\n\n\n\n

          Interested in learning about similar topics? Here are a few hand-picked blogs for you!
          <\/p>\n\n\n\n