1. Jan 30, 2015 #1

   MidgetDwarf

   

   Show that for any square matrix, the matrix A + ( A )^t is symmetric.
   
   My attempt. I know that A square matrix has the property that asub (ij). Where i=1,..., m and j=1,..,n.
   M=n(same number of rows and columns).
   
   I know that a transpose of a matrix means to interchange the rows with columns.
   
   What I do not understand what it means for a matrix to be symmetric?

    

   MidgetDwarf, Jan 30, 2015
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3. Jan 30, 2015 #2

   MidgetDwarf

   

   Sorry I forgot the t means the transpose if anyone is confused about my notation.

    

   MidgetDwarf, Jan 30, 2015
4. Jan 30, 2015 #3

   Nathanael

   

   Homework Helper

   A matrix B is symmetric if B^T=B
   
   In other words B_mn=B_nm for all entries (which also means it must be square). The diagonal entries can be anything because, for example, B₁₁=B₁₁ is always true. But B₁₂ must equal B₂₁, and so on.
   
   (It's easy to understand visually.)

    

   Nathanael, Jan 30, 2015

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