Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Calculus and Beyond Homework Help
The Transpose of a Matrix
Reply to thread
Message
[QUOTE=".Scott, post: 4517249, member: 489053"] Let [itex]B=A^{T}A[/itex]. Show that [itex]b_{ij}[/itex]=[itex]a^{T}_{i}[/itex][itex]a_{j}[/itex]. When you transpose [itex]A[/itex]You are flipping the rows and columns. When you multiply [itex]A^{T}A[/itex] you would generate each element [itex]b_{ij}[/itex] will be the dot product of row i of the first matrix and column j of the second matrix. Since the first matrix is the transposition of the second, row i of that transposition will be column i of the original. So each element will be the dot product of two column vectors: [itex]b_{ij}[/itex]=[itex]a_{i}[/itex]·[itex]a_{j}[/itex] Using matrix notation, this is: [itex]b_{ij}[/itex]=[itex]a^{T}_{i}[/itex][itex]a_{j}[/itex] [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Calculus and Beyond Homework Help
The Transpose of a Matrix
Back
Top