Explanation Given: A be an ( n × n ) matrix Approach: A matrix is symmetric if matrix A is equal to transpose of matrix A and matrix is skew symmetric if matrix A must be equal to negative of transpose of matrix A . Calculation: Let A be the ( n × n ) matrices. If matrix is symmetrix then A = A T and if it is skew symmetric then A = − A T . Consider, B = ( A + A T ) / 2 Now, ( A + A T ) T = A T + A Which means A = A T , therefore ( A + A T ) is symmetric and 1 2 ( A + A T ) is also symmetric. Consider, C = ( A − A T ) / 2 is skew symmetric which means A = − A T

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

5th Edition

ISBN: 9780134689531

Author: Lee Johnson, Dean Riess, Jimmy Arnold

Publisher: PEARSON

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‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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Chapter 5.3, Problem 29E

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Every (n×n) matrix can be expressed as the sum of a symmetric matrix and a skew symmetric matrix.

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Chapter 5.3, Problem 28E

Chapter 5.3, Problem 30E

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Chapter 5 Solutions

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - For u,v and w given in given Exercises 13,...Ch. 5.2 - Prob. 4E Ch. 5.2 - Prob. 5E Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - Prob. 7E Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...Ch. 5.2 - In Exercises 6-11, the given set is a subset of a...

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Every ( n × n ) matrix can be expressed as the sum of a symmetric matrix and a skew symmetric matrix.

Solution Summary: The author explains that every (ntimes n.) matrix can be expressed as the sum of a symmetric and skew-symmetric matrix.

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To show:

Every (n×n) matrix can be expressed as the sum of a symmetric matrix and a skew symmetric matrix.

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Chapter 5 Solutions

Every ( n × n ) matrix can be expressed as the sum of a symmetric matrix and a skew symmetric matrix.

Solution Summary: The author explains that every (ntimes n.) matrix can be expressed as the sum of a symmetric and skew-symmetric matrix.

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To show: Every (n×n) matrix can be expressed as the sum of a symmetric matrix and a skew symmetric matrix.

Want to see the full answer?

Chapter 5 Solutions

To show:

Every (n×n) matrix can be expressed as the sum of a symmetric matrix and a skew symmetric matrix.