Fundamentals of Matrix Algebra, 2011a

3
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O M
In the previous chapter we learned about matrix arithmec: adding, subtracng, and
mulplying matrices, finding inverses, and mulplying by scalars. In this chapter we
learn about some operaons that we perform on matrices. We can think of them as
funcons: you input a matrix, and you get something back. One of these operaons,
the transpose, will return another matrix. With the other operaons, the trace and
the determinant, we input matrices and get numbers in return, an idea that is different
than what we have seen before.
3.1 The Matrix Transpose
AS YOU READ ...
. . .
1. T/F: If A is a 3 × 5 matrix, then A T will be a 5 × 3 matrix.
2. Where are there zeros in an upper triangular matrix?
3. T/F: A matrix is symmetric if it doesn’t change when you take its transpose.
4. What is the transpose of the transpose of A?
5. Give 2 other terms to describe symmetric matrices besides “interesng.”
We jump right in with a definion.