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Matrix theory is the study of matrices as concrete objects, rather than as abstract linear operators between vector spaces (whose study belongs to linear algebra). For instance, this involves matrix factorizations and decompositions, nonnegative matrices and Perron-Frobenius theory, Schur complements, structured and special matrices, matrix functions and equations.

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Infinite matrices and the concept of "determinant"

There is a class of linear operators that have a determinant. They are, for some strange reason, known as "operators with a determinant". For Banach spaces, the essential details go along these line …
Andrew Stacey's user avatar