Rank 1 matrices are important in some computer algorithms and several theoretical contexts, including the singular value decomposition in Chapter 7. It can be shown that an m × n matrix A has rank 1 if and only if it is an outer product; that is, A = uv T for some u in ℝ m and v in ℝ n . Exercises 31-33 suggest why this property is true. 32. Let u = [ 1 2 ] . Find v in ℝ 3 such that [ 1 − 3 4 2 − 6 8 ] = u v T .
Rank 1 matrices are important in some computer algorithms and several theoretical contexts, including the singular value decomposition in Chapter 7. It can be shown that an m × n matrix A has rank 1 if and only if it is an outer product; that is, A = uv T for some u in ℝ m and v in ℝ n . Exercises 31-33 suggest why this property is true. 32. Let u = [ 1 2 ] . Find v in ℝ 3 such that [ 1 − 3 4 2 − 6 8 ] = u v T .
Solution Summary: The author explains how to find the vector vin R3.
Rank 1 matrices are important in some computer algorithms and several theoretical contexts, including the singular value decomposition in Chapter 7. It can be shown that an m × n matrix A has rank 1 if and only if it is an outer product; that is, A = uvT for some u in ℝm and v in ℝn. Exercises 31-33 suggest why this property is true.
32. Let
u
=
[
1
2
]
. Find v in ℝ3 such that
[
1
−
3
4
2
−
6
8
]
=
u
v
T
.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
HOW TO FIND DETERMINANT OF 2X2 & 3X3 MATRICES?/MATRICES AND DETERMINANTS CLASS XII 12 CBSE; Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=bnaKGsLYJvQ;License: Standard YouTube License, CC-BY