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Euclides in his work "Elements" presents geometric problems that would later be related to concepts of linear algebra.
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He introduced algebraic methods in his work, laying the foundations for solving linear equations.
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They developed analytical geometry, which unites algebra with geometry and establishes the foundations of linear algebra.
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Develops Cramer Rule for the solution of systems of linear equations.
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He develops the elimination method that bears his name to solve systems of linear equations. Advances are also made in matrix theory by mathematicians such as Augustin-Louis Cauchy.
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I develop the concept of vector spaces and Hilbert spaces, extending linear algebra to infinite dimensions and establishing a deep connection with quantum physics.
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Introduces quaternions, extending the concept of vectors into three dimensions.
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He formalizes matrix theory in his article "A Memoir on the Theory of Matrices", establishing the modern foundations of linear algebra.
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He proposes the Erlangen Program, unifying geometry and linear algebra under the study of symmetries and transformations.
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Linear algebra becomes a fundamental tool in linear programming, numerical analysis, and the development of algorithms for computers.