Abstract
This chapter presents quadratic and hermitian forms. The chapter also presents a theorem which states that the inverse of a nonsingular linear transformation is a nonsingular linear transformation. It discusses the composition of transformations and multiplication of matrices. A composition of two linear transformations is a linear transformation. If the linear transformations f1 and f2 have matrices A and B, respectively, then the composition f1f2 has matrix AB. A product of nonsingular matrices is nonsingular; a composition of nonsingular linear transformations is a nonsingular transformation. The chapter also discusses linear transformations of quadratic forms. The rank of a quadratic form is not changed by nonsingular transformations.
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