Matrix

This chapter introduces matrix to engineers who engage in practical engineering and gives the definition of matrix as well as algebraic manipulation rules. It describes principal types of matrix, namely square matrix, row matrix, column matrix, scalar, triangular matrix, diagonal matrix, unit matrix, zero matrix, transpose matrix, symmetric matrix, antisymmetric matrix, skew-symmetric matrix, and band matrix. The basic rule of matrix algebra is letting the linear transformation perform in a rather simple way. The chapter discloses the properties of matrix multiplication, of determinant, and of inverse matrix. It introduces partitioned matrix, orthogonal matrix and positive definite matrix. The derivative of matrix can be obtained by calculating the derivative of each element. The higher-order derivative of the matrix can be defined in the same way. In the finite element method, it is often required to calculate the integral of the product of several matrices.