Definitions for main diagonal
main di·ag·o·nal

Princeton's WordNetRate this definition:0.0 / 0 votes

1. main diagonal, principal diagonalnoun

   the diagonal of a square matrix running from the upper left entry to the lower right entry

WikipediaRate this definition:0.0 / 0 votes

1. Main diagonal

   In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix A {\displaystyle A} is the list of entries a i , j {\displaystyle a_{i,j}} where i = j {\displaystyle i=j} . All off-diagonal elements are zero in a diagonal matrix. The following four matrices have their main diagonals indicated by red ones: [ 1 0 0 0 1 0 0 0 1 ] [ 1 0 0 0 0 1 0 0 0 0 1 0 ] [ 1 0 0 0 1 0 0 0 1 0 0 0 ] [ 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ] {\displaystyle {\begin{bmatrix}\color {red}{1}&0&0\\0&\color {red}{1}&0\\0&0&\color {red}{1}\end{bmatrix}}\qquad {\begin{bmatrix}\color {red}{1}&0&0&0\\0&\color {red}{1}&0&0\\0&0&\color {red}{1}&0\end{bmatrix}}\qquad {\begin{bmatrix}\color {red}{1}&0&0\\0&\color {red}{1}&0\\0&0&\color {red}{1}\\0&0&0\end{bmatrix}}\qquad {\begin{bmatrix}\color {red}{1}&0&0&0\\0&\color {red}{1}&0&0\\0&0&\color {red}{1}&0\\0&0&0&\color {red}{1}\end{bmatrix}}\qquad }

ChatGPTRate this definition:0.0 / 0 votes

1. main diagonal

   The main diagonal of a matrix or a two-dimensional array is a diagonal that starts from the left top corner and ends at the right bottom corner. In other words, it is a line of elements from the top-left to bottom-right (or vice versa). It is also referred to as the principal or leading diagonal.

WikidataRate this definition:0.0 / 0 votes

1. Main diagonal

   In linear algebra, the main diagonal of a matrix is the collection of entries where is equal to . The main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. For example, the following matrix has 1s down its main diagonal: A square matrix like the above in which the entries outside the main diagonal are all zero is called a diagonal matrix. The sum of the entries on the main diagonal of a square matrix is known as the trace of that matrix. The main diagonal of a rectangular matrix is the diagonal which runs from the top left corner and steps down and right, until the right edge or the bottom edge is reached. The diagonal of a square matrix from the top right to the bottom left corner is called antidiagonal, counterdiagonal, secondary diagonal, or minor diagonal.

Matched Categories

1. • Diagonal

How to pronounce main diagonal?

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How to say main diagonal in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of main diagonal in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of main diagonal in Pythagorean Numerology is: 1

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=main diagonal
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Main_Diagonal
3. ^ ChatGPT
   https://chat.openai.com
4. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=main diagonal