I have been given M be an $m\times n$ matrix. I have to show that the matrix $M^TM$ is symmetric positive definite if and only if the columns of the matrix $M$ are linearly independent
My thoughts are as below $M^TM$ looks like a cholesky property and we know it is applicable as the matrix is SPD, still not able to connect how and which specific property to use to show if and only if columns of M are linearly independent...
Any hint as to how I should approach this...