Chapter 5 Geometric Properties of Linear Maps (GT)
How do we understand linear maps geometrically?
By the end of this chapter, you should be able to...
Describe how a row operation affects the determinant of a matrix.
Compute the determinant of a \(4\times 4\) matrix.
Find the eigenvalues of a \(2\times 2\) matrix.
Find a basis for the eigenspace of a \(4\times 4\) matrix associated with a given eigenvalue.
Before beginning this chapter, you should be able to...
Calculate the area of a parallelogram.
Recall and use the definition of a linear transformation.
Review: Section 3.1
Find the matrix corresponding to a linear transformation of Euclidean spaces.
Review: Section 3.2
Find all roots of quadratic polynomials (including complex ones).
Interpret the statement “\(A\) is an invertible matrix” in many equivalent ways in different contexts.
Review: Section 4.3