Provide definition of orthogonality

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Reference no: EM132414001

Questions -

Q1. Let A be a skew-symmetric n x n-matrix with entries in R, i.e. A^T = -A.

(a) Prove that u^TAu = 0 for every u ∈ Rⁿ.

(b) Prove that I_n + A is an invertible matrix.

Q2. Let two vectors x^→ = (x₁, x₂, ..., x_n) and y^→ = (y₁, y₂, ...., y_n).

a) Provide definition of orthogonality.

b) Prove that if x^→ and y^→ are mutually orthogonal, then they are linearly independent.

Q3. If G is a group and H is a subgroup of G, then H is a normal subgroup of G if ghg^-1 ∈ H for all g from the set of generators of G and for all h from the set of generators of H.

Reference no: EM132414001

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