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Unformatted text preview: Chapter 3: Linear algebra Problems in physics often lead to a set of linear equations. In solving linear equations is often convenient to use matrices and vectors. Matrices and vectors also occur frequently in the representation of states and linear operators in quantum mechanics. Determining the quantum states of a system can be reduced to solving an eigenvalue equation. Another example is coordinate transformations, which occurs in, for example, relativity and group theory, which is essential in particle physics but also crystallography amongst other areas. The vibrations of molecules and crystals can also be understood by solving large sets of linear equations. Its hard to overemphasize the importance of this subject! Patrick K. Schelling Introduction to Theoretical Methods Goals: By the end of this chapter you should be able to: I Represent a set of linear equations with matrices Patrick K. Schelling Introduction to Theoretical Methods Goals: By the end of this chapter you should be able to: I Represent a set of linear equations with matrices I Use elementary row reduction to solve a matrix equation Patrick K. Schelling Introduction to Theoretical Methods Goals: By the end of this chapter you should be able to: I Represent a set of linear equations with matrices I Use elementary row reduction to solve a matrix equation I Work with determinants Patrick K. Schelling Introduction to Theoretical Methods Goals: By the end of this chapter you should be able to: I Represent a set of linear equations with matrices I Use elementary row reduction to solve a matrix equation I Work with determinants I Use Cramers rule to solve matrix equations Patrick K. Schelling Introduction to Theoretical Methods Goals: By the end of this chapter you should be able to: I Represent a set of linear equations with matrices I Use elementary row reduction to solve a matrix equation I Work with determinants I Use Cramers rule to solve matrix equations I Work with vectors and vector algebra Patrick K. Schelling Introduction to Theoretical Methods Goals: By the end of this chapter you should be able to: I Represent a set of linear equations with matrices I Use elementary row reduction to solve a matrix equation I Work with determinants I Use Cramers rule to solve matrix equations I Work with vectors and vector algebra I Understand vector spaces, linear dependence/independence Patrick K. Schelling Introduction to Theoretical Methods Goals: By the end of this chapter you should be able to: I Represent a set of linear equations with matrices I Use elementary row reduction to solve a matrix equation I Work with determinants I Use Cramers rule to solve matrix equations I Work with vectors and vector algebra I Understand vector spaces, linear dependence/independence I Diagonalize a matrix Patrick K. Schelling Introduction to Theoretical Methods Goals:...
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 Spring '03
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