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...Mathematics concepts and foundations vol i matrices vectors determinants linear algebra tadao oda tohoku university japan keywords matrix determinant equation cramer s rule eigenvalue jordan canonical form symmetric vector space map contents their basic operations addition scalar multiplication of square cofactors the inverse systems equations eigenvalues a complex quadratic forms real orthogonal hermitian unitary spaces subspaces direct sum maps change bases properties unesco eolss system revisited quotient dual sample chapters tensor product exterior glossary bibliography biographical sketch summary down to earth introduction will be followed by encyclopedia life support results on abstract then introduced power merit seemingly useless abstraction make earlier more transparent easily understandable play important roles in applications unfortunately however limitation prevents description algorithmic computational aspects indispensable readers are referred references listed at end is ...