If A is triangular and no entry on the main diagonal is zero

muthuraman · May 1, 2015

A is invertible... How give me the proper explanation...

HallsofIvy · May 1, 2015

A matrix is invertible if and only if its determinant is 0. And for any triangular matrix, the determinant is simply the product of the numbers on the diagonal.

mathman · May 1, 2015

HallsofIvy said:

A matrix is invertible if and only if its determinant is 0. And for any triangular matrix, the determinant is simply the product of the numbers on the diagonal.

I presume you meant determinant is NOT zero.

HallsofIvy · May 1, 2015

mathman said:

I presume you meant determinant is NOT zero.

Yes, of course. Thank you!

mathwonk · May 8, 2015

also it should be obvious that the rows are independent. also the columns. so the map defined by the matrix is clearly injective.

If A is triangular and no entry on the main diagonal is zero

Discussion

Undergrad Spinor calculus

Undergrad Matrix representation of rank-2 spinors

Undergrad Looking for a paper about spinors

Undergrad Why are these cycles disjoint and of equal length?

On the Moore–Penrose inverse from a banal linear algebra viewpoint

Undergrad Correct constructed example of Abelian Monoid?

Undergrad Correct state row entries in the following Sequential machine?

Insights Why Vector Spaces Explain The World: A Historical Perspective

Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

If A is triangular and no entry on the main diagonal is zero

Discussion

Similar threads

Find LU-Factorization of A with 1's Along Main Diagonal of L

Similar matrices and main diagonal summation?

Zero matrix with non-zero above diagonal

High School How do I check if a 1x1 matrix is diagonal, lower/upper triangular?

Undergrad Calculating the Main Diagonal of a Parallelepiped from Origin to Opposite Vertex

Graduate Help Diagonal matrix similar to upper triangular matrix?

Undergrad Understanding Upper Triangular, Lower, and Diagonal Matrices

Block triangular matix has rank >= ranks of diagonal blocks?

How to Show that L is a Diagonal Matrix for Invertible Triangular Matrices LU=A?

Proving the Nilpotency of Square Triangular Matrices with Zero Diagonal Entries