Then n x n matrix A= [aij] is called a diagonal matrix if aij= 0 when i =/= j. Verify that the product of two n x n diagonal matrices is again a diagonal matrix, and give a simple rule for determining this product.
Q. A second order tensor has components ■(2&1&0@1&-3&-1@0&-1&2) in OX1X2X3. The transformation between the coordinates X1, X2, X3 and X1’ , X2’ , X3’ is defined by
X1’=1/3 (2x1+2x2-x3)
X2’=1/3 (2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)
(i)Find its components in the new system OX1’X2’X3’.(By using Matrix Formula).
(ii) Compute A’32 in the new system.(By using component formula)
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