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Ancient Egyptians and Babylonians: Use of primitive geometric and algebraic methods to solve systems of linear equations. -
Ancient China: "The Nine Chapters on the Mathematical Art" (Jiuzhang Suanshu) describes methods of solving linear systems involving matrices. -
Islamic mathematicians: Al-Khwarizmi and other mathematicians develop methods for solving linear and quadratic equations. Their work is translated and expanded in the Renaissance. -
Gerolamo Cardano: Develops methods for solving cubic and fourth equations, which contributes to the development of algebraic theory. -
René Descartes: Introduces the modern notation for coordinates in the Cartesian plane, which establishes the basis for the representation of linear systems. -
Leonhard Euler: Develops the concept of matrices and their operations in an algebraic context, precursor of modern linear algebra. -
Nicolas-Louis de Lacroix: Publishes works on matrices and determinants, extending the theory of matrices. -
William Rowan Hamilton: Introduces quaternions, an extension of complex numbers that influences the development of linear algebra and the theory of vector spaces. -
Arthur Cayley: He published a fundamental work on matrices, in which he introduced the modern definition of matrices and the operations that can be performed with them. -
Ferdinand Frobenius: He made significant contributions to matrix theory and to the formulation of spectral theory, including Frobenius's theorem. -
David Hilbert: Develops the theory of Hilbert spaces, extending linear algebra to infinite-dimensional spaces and contributing to the theory of linear operators. -
John von Neumann and others: They develop the theory of Hilbert spaces and the theory of operators in the context of quantum mechanics, applying concepts of linear algebra. -
Software and algorithm development: With the advancement of computing, efficient algorithms are developed for matrix manipulation and the resolution of linear systems, making linear algebra fundamental in areas such as artificial intelligence, data science and engineering.