Question

how are these symmetric matrices.. I am confuse how they explained it

Answer 1

@Nnesha

Answer 2

let's take the 2x2 matrix first

Answer 3

to start the transpose: the first row becomes the first column of the transpose, so:

Answer 4

then the second row becomes the second column, like so:

Answer 5

producing two equal matrices

does this make sense?

Answer 6

oh okay that makes sense but where it says symmetric matrix ... the main diagnal has to be all 0's?

Answer 7

oh

there are two types, just plain "symmetric" and "skew-symmetric"

for just plain symmetric the transpose is equal to itself

for skew-symmetric the transpose is equal to the negative of itself, and in this case only the diagonals must all be 0's

Answer 8

oh, was that a symmetric example that you posted?

Answer 9

yeah the example I posted was symmetric

Answer 10

the reasoning for the 0-diagonals:

aij and aji are corresponding terms on skew-symmetric matrices (the term in row i and column j ---> turns into ---> the term in row j and column i of the transpose)

for a skew-symmetric matrices, aij = -aji (by definition)

on the diagonals, i = j

so aii = -aii

Answer 11

(and that's only true for aii = 0)

Answer 12

oh okay