Abstract
This chapter discusses singular values and estimates of proper values of matrices. Linear transformations are analogous to complex numbers in many ways. Among the more important similarities are these. The operation that leads from a matrix to its adjoint corresponds to obtaining the conjugate of a complex number. Hermitian transformations play the part of real numbers. A unitary transformation is similar to a complex number of unit absolute value. The analogy between linear transformations and complex numbers becomes deeper considering the proper values of transformations or matrices. A Hermitian transformation has only real proper values, and the proper values of nonnegative transformations are nonnegative. The proper values of a unitary transformation have modulus one.
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