Use the decomposition result (1.2.10) to express a_ij from Exercise 1.1 in terms of the sum of symmetric and antisymmetric matrices. Verify that a(_ij) and a[_ij] satisfy the conditions given in:
the last paragraph.

Equation 1.2.10

Data from exercise 1.1

For the given matrix/vector pairs, compute the following quantities: a_ii, a_ija_ij, a_ija_jk, a_ijb_j, a_ijb_ib_j, b_ib_j, b_ib_i. For each case, point out whether the result is a scalar, vector or matrix. Note that aijbj is actually the matrix product [a]{b}, while a_ija_jk is the product [a][a].

Transcribed Image Text:

aij z (aij + aji) +z (aij aji) = a(ij) + a[i]