Introduction to bilinear forms
... We call a bilinear form B nondegenerate if the discriminant of B is nonzero. To be able to apply the properties of the discriminant and nondegeneracy, we must first understand orthogonality. Given vectors v, w ∈ V we say that v is orthogonal to w (denoted v⊥w) if B(v, w) = 0. We would like to descri ...
... We call a bilinear form B nondegenerate if the discriminant of B is nonzero. To be able to apply the properties of the discriminant and nondegeneracy, we must first understand orthogonality. Given vectors v, w ∈ V we say that v is orthogonal to w (denoted v⊥w) if B(v, w) = 0. We would like to descri ...
Matlab Tutorial I
... The former is accomplished with the * operator, just as if you were multiplying two scalars together. The latter is accomplished with the .* operator (a period before the asterisk). So [1 2 3] .* [4 5 6] = [4 10 18] but [1 2 3] * [4 5 6]’ = 32 (note the transpose operator) and [1 2 3] * [4 5 6] is ...
... The former is accomplished with the * operator, just as if you were multiplying two scalars together. The latter is accomplished with the .* operator (a period before the asterisk). So [1 2 3] .* [4 5 6] = [4 10 18] but [1 2 3] * [4 5 6]’ = 32 (note the transpose operator) and [1 2 3] * [4 5 6] is ...
Yet Another Proof of Sylvester`s Identity
... Despite the fact that the importance of Sylvester’s determinant identity has been recognized in the past, we were able to find only one proof of it in English (Bareiss, 1968), with reference to some others. (Recall that Sylvester (1857) stated this theorem without proof.) Having used this identity, ...
... Despite the fact that the importance of Sylvester’s determinant identity has been recognized in the past, we were able to find only one proof of it in English (Bareiss, 1968), with reference to some others. (Recall that Sylvester (1857) stated this theorem without proof.) Having used this identity, ...
