Topic: Dual Spaces and Bilinear Forms

Why the Dual Map Has the Transposed Matrix

The Dual Map of a Linear Transformation

The Dual Space and Its Dimension

The Dimension of an Annihilator

Symmetric Bilinear Forms and Quadratic Forms

Sylvester’s Law of Inertia

Similarity Versus Congruence for Forms

Radicals and Orthogonality for Bilinear Forms

Maximal Positive Subspaces and Inertia

Linear Functionals and Their Kernels