The Magic of the Gramian (Gram Determinant in an Inner Product Space)
An examination of the Gramian (Gram determinant, or determinant of the Gram matrix in an inner product space), including:
Basic algebraic and geometric properties
Relationship to normal determinant functions and n-dimensional volume
Measurement of height / distance (orthogonal projection)
Generalized Pythagorean theorem
Generalized Hadamard inequality
Generalization of the determinant to linear maps between different inner product spaces (equivalently, to rectangular matrices), with connections to the singular value decomposition
"Ah, excuse me, Vice-president Coco, no one cares about your Gammy." - George Costanza
More videos on determinants: • Determinants
More videos on linear algebra: • Linear and Multilinear Algebra