Matrix | Tensor Analysis Answers

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.

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

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

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

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

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

For the following matrix calculate the determinant:
{{5,3,7},{1,0,1},{9,6,4}}

Evaluate the following:

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

Given the following:
A = 3 * 3
B = 2 * 4
C = 4 * 3
D = 3 * 2

Which of the following are defined:
A * D
D * B
A * D^T
C * D + A * D^T
A * B
A * D^T + C

Evaluate the following problem:

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