Vectors a basis in R is given by any set of linearly independent vectors ei, (e1, e2, e3) From now on we will assume that these basis vectors are orthonormal. i.e they have a unit length and they are orthogonal with respect to each other This can be expressed using dot products 1 =0,ele3=0, Using indicial notation we can write these expression in very succinct form as follows In the last expression the symbol diy is defined as the Kronecker delta if i 0ifi≠ Example a10;=a101+a2021+a3531, a1613+a20623+a30 a1+a20+a30 a10+a21+a30, a10+a20+a3 or more succinctly: a, i=a, i.e., the Kronecker delta can be thought of an Index replacer A vector v will be represented as viei=Ue1 Uge2+ U3e3 3� Vectors A basis in R3 is given by any set of linearly independent vectors ei, (e1, e2, e3). From now on, we will assume that these basis vectors are orthonormal, i.e., they have a unit length and they are orthogonal with respect to each other. This can be expressed using dot products: e1.e1 = 1, e2.e2 = 1, e3.e3 = 1, e1.e2 = 0, e1.e3 = 0, e2.e3 = 0, ... Using indicial notation we can write these expression in very succinct form as follows: ei.ej = δij In the last expression the symbol δij is defined as the Kronecker delta: δij = 1 if i = j, 0 if i �= j Example: aiδij =a1δ11 + a2δ21 + a3δ31, a1δ12 + a2δ22 + a3δ32, a1δ13 + a2δ23 + a3δ33 =a11 + a20 + a30, a10 + a21 + a30, a10 + a20 + a3 =a1, a2, a3 or more succinctly: aiδij = aj , i.e., the Kronecker delta can be thought of an “index replacer”. A vector v will be represented as: v = viei = v1e1 + v2e2 + v3e3 3