The transpose of a matrix is an operator that flips over its diagonal. i.e, rows and columns of a matrix are interchanged to get a transpose of the matrix.
Now consider the example given below:
Did you notice how the matrix looks after changing the rows into columns or the columns into rows?
Yes, it looks the same as the input matrix. This type of matrix is called a symmetric matrix.
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Now let us learn some more examples.
One is with a 3*3 identity matrix:
This concludes that every square identity matrix with at least 2 rows and 2 columns is symmetric.
Now consider a diagonal matrix: i.e., a matrix where all other entries except diagonals are zero.
This concludes that every square diagonal matrix with at least 2 rows and 2 columns is symmetric.
a represents the entry of a matrix in the ith row and jth column, ‘m’ denotes the number of rows and ‘n’ denotes the number of columns in a matrix, then
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