Preface to the Paradigms 4, 5, and 6: Matrices and Operators

The winter Preface is a week-long math primer in matrix methods needed for the Spins, Waves, and Central Forces paradigms. Students are assumed to have already had an introduction to linear algebra, but student who have not can still be successful. This course serves to review matrix algebra and frames the discussion of matrices in the context of vectors spaces and linear transformations. The course contains a sequence of two small group activities that emphasize rotation matrices, eigenvectors and eigenvalues, and the link between the type of transformation and the value of the determinant.

Textbook: The course content for this book is covered in any linear algebra text (except for bra-ket notation) and/or any mathematical methods text.

Sample Syllabus: Winter 2008

Course Contents

Unit: Matrices and Vectors

Tangible Metaphor for Complex Vectors (10 minutes)

Matrix Manipulations (45 minutes)

Introduction to Bra-ket notation (15 minutes)

Unit: Operators and Transformations in Linear Systems

Linear Transformations (1 1/2 hr)

Rotation Matrices in 2 and 3 Dimensions (10 min)

Properties of Linear Vector Spaces (30 min)

Matrix Components (40 min)

Unit: Eigenvalues and Eigenvectors

Eigenvalues & Eigenvectors (2 hr)

Special Properties of Hermitian Matrices (40 min)

Commuting Matrices (10 min)

Preface SWBQs

FIXME - In process of editing. See Master SWBQ List at “Pedagogy” → “Small Whiteboard Questions”


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