Rank Of Gram Matrix

Algebra Level 5

Let \(v_1, \cdots, v_n \in \mathbb{R}^m\) be a collection of vectors. The Gram matrix of this collection is defined to be the \(n\)-by-\(n\) matrix whose entry in the \(i^\text{th}\) row and \(j^\text{th}\) column is \(a_{ij} = v_i \cdot v_j\), where \(\cdot\) denotes the dot product.

Consider the Gram matrix \(G\) of the collection: \[v_1 = (1,2,1),\] \[v_2 = (-3,5,1),\] \[v_3 = (0,-3,6),\] \[v_4 = (4,-2,0).\] What is the rank of \(G\)?

×

Problem Loading...

Note Loading...

Set Loading...