A Matlab Workbook on the Pedagogy of Generalized Eigenvectors

作者：Shankar P M^*

来源：Computer Applications in Engineering Education, 2017, 25(3): 411-419.

DOI：10.1002/cae.21808

• linear algebra
• differential equations
• generalized eigenvectors
• fundamental matrix
• matrix exponential
• null space
• Matlab
• pedagogy

The pedagogical aspects of generalized eigenvectors are demonstrated using a Matlab workbook. With the simple input of a square matrix, the workbook displays the theoretical background, classifies the matrix as defective or non-defective, and processes the matrix further. It obtains the algebraic and geometric multiplicities, and identifies the eigenvalues making the matrix defective. The generalized eigenvectors are calculated and displayed, every step fully annotated to bring out the didactic aspects. These include reiteration of the multiplicities and association of specific eigenvalues with eigenvector and generalized eigenvectors. Unlike simple Matlab scripts that provide eigenvalues and eigenvectors without validation, the workbook generates the matrix exponential using eigenvalues and eigenvectors and compares it to matrix exponentials obtained using inverse Laplace transforms and directly in Matlab. The workbook with annotations, verification and displays matching instructor's classroom work can be expected to enhance the understanding of eigenvectors, generalized eigenvectors, multiplicities, fundamental matrix, and matrix exponential.

• 出版日期2017-5