Please follow the rules of posting in this forum - enunciated at:Not sure how to answer the following problem:
Show that any square matrix can be written as the sum of a symmetric and a skew symmetric matrix.
Please follow the rules of posting in this forum - enunciated at:
https://www.freemathhelp.com/forum/threads/read-before-posting.109846/
Please share your work/thoughts with us - so that we know where to begin to help you. Also include the context - topic being taught in class now.
Please post the EXACT problem as it was presented to you.
To start with, please answer:
What is symmetric matrix?
What is skew-symmetric matrix?
HINTS: Suppose that \(\displaystyle A\) is an \(\displaystyle n\times n\) real matrix.Not sure how to answer the following problem:
Show that any square matrix can be written as the sum of a symmetric and a skew symmetric matrix.
HINTS: Suppose that \(\displaystyle A\) is an \(\displaystyle n\times n\) real matrix.
Consider the matrices \(\displaystyle B=\tfrac{1}{2}(A+A')~\&~C=\tfrac{1}{2}(A-A')\)
Sorry that is for transpose. See here.
HINTS: Suppose that \(\displaystyle A\) is an \(\displaystyle n\times n\) real matrix.
Consider the matrices \(\displaystyle B=\tfrac{1}{2}(A+A')~\&~C=\tfrac{1}{2}(A-A')\)
As you do your study, you will find that two different textbooks can use a symbol in exactly opposite & different ways. That is just the curse of different authors/professors. In grad school at the same university I had three major professors that each used a different notation for set intersection: \(\displaystyle AB,~A\cdot B,\text{ or }A\cap B\).Thought \(\displaystyle A^T \) was the transpose... I've been slowly studying linear algebra on my spare time, following a very dense book and I haven't reach vector spaces yet... So I've no idea where you are trying to go with that example you posted in the link.
As you do your study, you will find that two different textbooks can use a symbol in exactly opposite & different ways. That is just the curse of different authors/professors. In grad school at the same university I had three major professors that each used a different notation for set intersection: \(\displaystyle AB,~A\cdot B,\text{ or }A\cap B\).
As for this case it you question does not depend on vector spaces. Use the link to construct symmetric and skew symmetric matrices.