the part of algebra that deals with the theory of linear equations and linear transformation
Linear algebra is a branch of mathematics concerned with the study of vectors, with families of vectors called vector spaces or linear spaces, and with functions that input one vector and output another, according to certain rules. ...
may be a course in matrix theory (MW, Wik) or a course in linear transformations in a more abstract setting.
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in which the specific properties of vector spaces are studied (including matrices);