When we write vectors as matrices, we tend to write an $n$-dimensional vector vector as $n \times 1$ column matrix. We emphasize that the gradient vector is defined only for scalar-valued functions. For vector valued functions, we will stick with viewing the derivative as a matrix.
Gloomy Addiction Relapse Statistics. Drug and alcohol rehab statistics show that the percentage of people who will relapse after a period recovery ranges from 50% to 90%. This is a frightening statistic and it is often used as justification for those who wish to carry on with their addiction.
Long-Term Recovery. Although it is difficult to predict the exact stroke recovery time frame, most improvements happen within the first six months. Patients may continue to improve after the six-month period if they have a great deal of support from family, friends, and doctors. After the initial few days of recovery: