To explore the various kind of matrices, matrix multiplication, identity matrix, characteristic equation, minimal polynomial and diagonalization, my paper investigates matrices and algebraic operations defined on them...To explore the various kind of matrices, matrix multiplication, identity matrix, characteristic equation, minimal polynomial and diagonalization, my paper investigates matrices and algebraic operations defined on them. These matrices may be viewed as rectangular array of elements where each entry depends on two subscripts. System of linear equations and their solutions may be efficiently investigated using the language of matrices. Furthermore, certain abstract objects introduced in the end of my papers, such as I-matrix, J-matrix, Transprocal of certain matrix, transpose of transprocal matrix, i.e. transprocose matrix, super orthogonality, super unitary, trans othogonaliity, and trans orthoprocal, can be represented by this matrix. On the other hand, the abstract treatment of linear algebra presented later will give us a new insight into the structure of these matrices. The entries in our matrices will come from some arbitrary, but fixed, field K.展开更多
文摘To explore the various kind of matrices, matrix multiplication, identity matrix, characteristic equation, minimal polynomial and diagonalization, my paper investigates matrices and algebraic operations defined on them. These matrices may be viewed as rectangular array of elements where each entry depends on two subscripts. System of linear equations and their solutions may be efficiently investigated using the language of matrices. Furthermore, certain abstract objects introduced in the end of my papers, such as I-matrix, J-matrix, Transprocal of certain matrix, transpose of transprocal matrix, i.e. transprocose matrix, super orthogonality, super unitary, trans othogonaliity, and trans orthoprocal, can be represented by this matrix. On the other hand, the abstract treatment of linear algebra presented later will give us a new insight into the structure of these matrices. The entries in our matrices will come from some arbitrary, but fixed, field K.
