Definition of Principal diagonal

1. Noun. The diagonal of a square matrix running from the upper left entry to the lower right entry.

Exact synonyms: Main Diagonal
Generic synonyms: Diagonal



Principal Diagonal Pictures

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Literary usage of Principal diagonal

Below you will find example usage of this term as found in modern and/or classical literature:

1. The American Mathematical Monthly by Mathematical Association of America (1922)
"Explicitly, let a = The scalar, a, will be said to be "real" when and only when all of the elements above the principal diagonal vanish and when furthermore ..."

2. An Elementary Treatise on the Theory of Determinants: A Text-book for Colleges by Paul Henry Hanus (1903)
"Also let (72 denote any product of the elements of the principal diagonal of Д("' taken 2 and 2 ; C3 any product of those elements taken 3 and 3 ; and, ..."

3. Mathematical Questions and Solutions (1894)
"Let 8',, be a determinant identical with 8,, except that the first element of the principal diagonal is D2 + 2k instead of I!2 + k. 8'n = AB-iA,,-i, ..."

4. A treatise on the theory of determinants: With Graduated Sets of Exercises by Thomas Muir (1882)
"By multiplying an element of the principal diagonal by its co-factor we obtain ... This co-factor, however, has its principal diagonal composed of elements ..."

5. The Century Dictionary: An Encyclopedic Lexicon of the English Language by William Dwight Whitney (1890)
"The diagonal running from the upper left hand to the lower right hand corner is called the principal diagonal. Constituents symmetrically situated with ..."

6. Primitive Groups by William Albert Manning (1921)
"1=1 A substitution in which all the coefficients above the principal diagonal are zero is in normal form or is a normal substitution. ..."

7. An Introduction to the Theory of Multiply Periodic Functions by Henry Frederick Baker (1907)
"NOTE I. THE REDUCTION OF A MATRIX TO ONE HAVING ONLY principal diagonal ELEMENTS. LET a be a matrix of integers of m rows and n columns ; consider the ..."

8. An Introduction to the Theory of Multiply Periodic Functions by Henry Frederick Baker (1907)
"NOTE I. THE REDUCTION OF A MATRIX TO ONE HAVING ONLY principal diagonal ELEMENTS. LET a be a matrix of integers of m rows and n columns ; consider the ..."

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