In a column-stochastic matrix used for Markov chains, what must the sum of each column be?

Show answer

One

Column-stochastic matrices ensure that the total probability is conserved during transitions. Each entry represents the probability of moving from one state to another, so the sum of possibilities must equal 1.

Also asked as:

What is the required sum for each individual column in a column-stochastic matrix?

Would you remember this in 6 months?

Trivia Forge uses spaced repetition so facts stick. Free, no signup needed.

Turn on Linear Algebra practice →

More Linear Algebra trivia

In a Jordan Canonical Form block, what values are located on the main diagonal?
In a Markov chain with transition matrix P, what do we call a probability vector v that satisfies the equation vP = v?
In a Markov chain, what do we call a square matrix used to describe the transitions of a system?
In a Markov chain, what is the name for a matrix where every column sums to 1 and all entries are non-negative?
In a right stochastic transition matrix of a Markov chain, what must the entries in each row sum to?
In a system of linear equations Ax=0, if the coefficient matrix has more columns than rows (m < n), the system must have at least one of what type of variable?

See all 145 →