The diagonal of a square matrix refers to all elements in a line from the top-left to the bottom- right of the matrix. For example, in the 3 x 3 matrix below, all diagonal entries are 1 where off-diagonal entries are 0: [1 0 0] 1. 0 0 1 Note that the only entry in a 1 x 1 matrix is on the diagonal. The upper-diagonal of a matrix are all entries which are on the diagonal or above. For example, in the 3 x 3 matrix below, all upper-diagonal entries are 1 where non-upper-diagonal entries are 0: [1 1 1] 0 1 1 0 0 1 Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries.
The diagonal of a square matrix refers to all elements in a line from the top-left to the bottom- right of the matrix. For example, in the 3 x 3 matrix below, all diagonal entries are 1 where off-diagonal entries are 0: [1 0 0] 1. 0 0 1 Note that the only entry in a 1 x 1 matrix is on the diagonal. The upper-diagonal of a matrix are all entries which are on the diagonal or above. For example, in the 3 x 3 matrix below, all upper-diagonal entries are 1 where non-upper-diagonal entries are 0: [1 1 1] 0 1 1 0 0 1 Use induction to show that an n x n matrix has n(n + 1)/2 upper-diagonal entries.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:The diagonal of a square matrix refers to all elements in a line from the top-left to the bottom-
right of the matrix. For example, in the 3 x 3 matrix below, all diagonal entries are 1 where
off-diagonal entries are 0:
[1 0 0
0 1 0
0 0 1
Note that the only entry in a 1 x 1 matrix is on the diagonal.
The upper-diagonal of a matrix are all entries which are on the diagonal or above. For example,
in the 3 x 3 matrix below, all upper-diagonal entries are 1 where non-upper-diagonal entries are 0:
[1 1 17
0 1 1
0 0 1
Use induction to show that an n xn matrix has n(n + 1)/2 upper-diagonal entries.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
