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Matrix | Tensor Analysis

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.

Matrix | Tensor Analysis

Show that eigen values of hermitian matrice are real numbers. Expalin.

Matrix | Tensor Analysis

Suppose A is a square matrix such that det(A0 = 2 and det(3A the power of t) = 18 then find the order of matrix A

Matrix | Tensor Analysis

Suppose A is a square matrix such that det(A)= 2 and det(3At)= 18 then find the order of matrix A

Matrix | Tensor Analysis

What are covariant and contravariant vectors? Show that acceleration is a contravariant vector.

Matrix | Tensor Analysis

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)

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)

Matrix | Tensor Analysis

Q. Write transformation equations for a second order tensor Aij w.r.t this transformation and verify A’ii=Aii

Matrix | Tensor Analysis

WHAT IS MEAN BY (0,2) and (2,0) (1,1) tensor.

Matrix | Tensor Analysis

For the following matrix calculate the determinant:

{{5,3,7},{1,0,1},{9,6,4}}

{{5,3,7},{1,0,1},{9,6,4}}

Matrix | Tensor Analysis

Evaluate the following:

{{1,2,3},{4,5,6},{7,8,9}} * {{7,4},{6,4},{5,3}}

{{1,2,3},{4,5,6},{7,8,9}} * {{7,4},{6,4},{5,3}}