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en.wikipedia.org/wiki/Diagonal_matrix

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero. The term usually refers to square matrices.An example of a 2-by-2 diagonal matrix is []; the following matrix is a 3-by-3 diagonal matrix: [].An identity matrix of any size, or any multiple of it, will be a diagonal matrix.

mathworld.wolfram.com/DiagonalMatrix.html

The diagonal matrix with elements can be computed in the Wolfram Language using DiagonalMatrix[l]. The determinant of a diagonal matrix given by is . This means that , so for , 2, ..., the first few values are 1, 2, 6, 24, 120, 720, 5040, 40320, ... (OEIS A000142). Given a matrix equation of the form

en.wikipedia.org/wiki/Determinant

The rule of Sarrus is a mnemonic for the 3 × 3 matrix determinant: the sum of the products of three diagonal north-west to south-east lines of matrix elements, minus the sum of the products of three diagonal south-west to north-east lines of elements, when the copies of the first two columns of the matrix are written beside it as in the illustration.

math.stackexchange.com/questions/1243237/prove-the...

Prove that the determinant of an upper triangular matrix is the product of its diagonal entries. What I have so far: We will prove this by induction for an $n ...

answers.yahoo.com/question/index?qid=20110707091335AAfoVUH

To show that this is true for a (k+1) x (k+1) diagonal matrix (call it A), first expand across the first row. So, the determinant of A equals a(1,1) * [determinant of a k x k diagonal matrix], since all other entries on the first row of A are 0's. However, we know by inductive hypothesis that the determinant of a k x k matrix

yutsumura.com/determinant-of-matrix-whose-diagonal-entries...

Determinant of matrix whose diagonal entries are 6 and 2 elsewhere. Determinant if the product of eigenvalues. Harvard University Linear Algebra exam problem.

www.khanacademy.org/math/algebra-home/alg-matrices/alg...

Sal shows a "shortcut" method for finding the determinant of a 3x3 matrix. ... Determinant of a 3x3 matrix: shortcut method (2 of 2) About Transcript. ... I will take the same matrix, matrix A and take its determinant again but I will do it using a different technique, either technique is valid so here we saying what is the determinant of the ...

people.richland.edu/.../lecture/m116/matrices/determinant.html

6.4 - The Determinant of a Square Matrix. ... The determinant of a triangular matrix or a diagonal matrix is the product of the elements on the main diagonal. Elementary Row Operations. There were three elementary row operations that could be performed that would return an equivalent system. With determinants, since the determinant of a ...

www.math.lsa.umich.edu/~hochster/419/det.html

Fact 6. An n by n matrix with a row of zeros has determinant zero. Here is why: expand with respect to that row. Fact 7. The determinant of a lower triangular matrix (or an upper triangular matrix) is the product of the diagonal entries. In particular, the determinant of a diagonal matrix is the product of the diagonal entries.

cljavacode.blogspot.com/2017/06/matrix-determinant-by...

A matrix diagonal transformation method is preferred over minor or cofactor of matrix method while finding determinant of the matrix's size over 3x3. The matrix A is converted into Diagonal matrix D by elementary row operation or reduction and then product of main diagonal elements is called determinant of the matrix A. Read matrix A