Recent content by abbasb

  1. A

    Proving Orthonormal Basis for an Orthogonal Matrix

    I've been trying to figure out how, but I just can't seem to think of a way...anymore advice?
  2. A

    Proving Orthonormal Basis for an Orthogonal Matrix

    Homework Statement Prove: if an n × n matrix A is orthogonal (column vectors are orthonormal), then the columns form an orthonormal basis for R^n. (with respect to the standard Euclidean inner product [= the dot product]). Homework Equations None. The Attempt at a Solution I...
  3. A

    Inner Product Spaces of 2x2 Matrix

    But shouldn't I be looking for a 2x2 matrix such that <U,U> = u1^2 + 2(u2.u3) + u4^2 < 0? And the only way I could find such a matrix is through trial and error?
  4. A

    Inner Product Spaces of 2x2 Matrix

    Sorry, its supposed to be <U,V> = u1.v1 + u2.v3 + u3.v2 + u4.v4 and U and V are supposed to be matrices...couldn't find a better way to show them as so.
  5. A

    Inner Product Spaces of 2x2 Matrix

    Homework Statement Show that <U,V> = u1.v1 + u2.v3 + u2.v3 + u4.v4 is NOT an inner product on M[SIZE="2"]2x2Homework Equations U: row 1 = [u1 u2] row 2 = [u3 u4] V: row 1 = [v1 v2] row 2 = [v3 v4] The Attempt at a Solution As I went through each of the axioms, I found that they were all...