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Carl Friedrich Gauss
Carl Friedrich Gauss
In his theory of the biquadratic residuals, he had constructed a rigorous algebra of the complex numbers. -
William Rowan Hamilton
William Rowan Hamilton
He dealt with vectors and created a system of
complex numbers he called Quaternions, as the first and only non-commutative division ring over the reals. -
Hermann Günther Grassmann
Hermann Günther Grassmann
Together with Hamilton, the notions and axiomatization of vector and vector space are attributed to them, considered the master of linear algebra, Grassmann introduces the geometric and linear product; he introduces notions of linear independence, as well as that of
dimension of a vector space. -
James Joseph Sylvester
James Joseph Sylvester
He was the first to use the term “matrix", he defined it as a
"quadrilateral arrangement of terms", and the important concept of "range"; many terms are due to it such as: invariant, covariant, contravariant, cogradient, among others. -
Charles Hermite
Charles Hermite
He is credited with solving the equations of the fifth degree, the reduced form of a linear substitution, and the mathematical entities called Hermitian. Together with Sylvewster and Cayley the theory of invariants was created and for this reason they are known by the nickname of the "invariant trinity". -
Arthur Cayley
Arthur Cayley is considered to be the founder of matrix theory; one of his main merits was the introduction of the basic operations of addition and multiplication of matrices, he proved that matrix multiplication is associative and introduces the powers of a matrix, as well as symmetric and antisymmetric matrices -
Camille Jordan
Camille Jordan
In the "Treatise on Substitutions and Algebraic Equations" he studies
a canonical form for linear substitutions over finite fields of prime order. In this context, what we know today as the canonical Jordan form appears for the first time. -
David Hilbert
David Hilbert
He considered that the linear operators acted
over certain infinite-dimensional vector spaces, here arose the notion of a quadratic form in an infinity of
variables, and it was in this context that Hilbert first used the term spectrum to refer to a complete set of eigenvalues.