Measuring Cylinder

Good lumber is hard to find these days.

Y, that gives me my 47 by one vector. This is a 47 dimensional vector.

And so you can make lumber of any size for making a table, or you can make your own house.

Suppose we have a twenty dimensional cube.

It's of index signed from zero. That is another n plus 1 dimensional vector.

And the result of this product is going to be an n dimensional vector y.

In fact, more generally, this is an in dimensional feature back there.

The result will be a M dimensional vector, which we'll put there.

With this notation X2 is a four dimensional vector.

So this is now a n 1 dimensional feature vector, but

I'm going to take the third column, multiply it by this matrix, I get a M dimensional vector.

Finally, I copy the 3 dimensional symbol for my policy straight into the 2 dimensional array.

Obviously this is a 1 dimensional example and not 2 dimensional as the picture suggests over here.

And so this thing on the right this thing on the right overall, this is a 4 by 1 dimensional matrix, was a 4 dimensional vector.

So, each of the training example x(i) may looks like a vector like this, that is a n 1 dimensional feature vector.

Each training example gives me a feature vector like this. say, sort of n 1 dimensional vector.

The key insight here is to go from the 3 dimensional full policy to a 2 dimensional array I had to run the policy.

) A block of n letters is then considered as a vector of n dimensions, and multiplied by a n x n matrix, modulo 26.

This is a four dimensional vector, or a 4 x 1 matrix, and so the result of this, the result of this product is going to be a three dimensional vector.

It takes the insight from the OXO measuring cup that you can measure from above and improves upon it in two ways

The Schläfli symbol for the dual polytope is just the original symbol written backwards 3, 3 is self dual, 3, 4 is dual to 4, 3 , 4, 3, 3 to 3, 3, 4 and so on.

For example, if you imagine that you have m equals 10 training examples and that you have n equals 100 features, then you're trying to fit a parameter vector theta, which is (n 1) dimensional, so it's a 101 dimensional you're trying to fit a 101 parameters from just 10 training examples.

Today, we're going to explore what makes an interface easy, hard, or natural, and we're going to do it by starting with something really simple a measuring cup.

The parameters of this model are theta0 through theta n, but instead of thinking of this as n separate parameters, which is valid, I'm instead going to think of the parameters as theta where theta here is a n 1 dimensional vector.

In the problem that we are interested in, Theta is no longer just a real number, but, instead, is this n 1 dimensional parameter vector, and, a cost function J is a function of this vector value or Theta 0 through

So the matrix A is a m by n dimensional matrix, so m rows and n columns and we are going to multiply that by a n by 1 matrix, in other words an n dimensional vector.

Then, I'm going to take the second column of B, right, so, this is another n by one vector, so, this column here, this is right, n by one, those are n dimensional vector, gonna multiply this matrix with this n by one vector.

Here, I'm going to treat theta as a vector so, there's an N 1 dimensional vector.

The vector Y is obtained by taking all all the labels, all the correct prices of houses in my training set, and just stacking them up into an M dimensional vector, and that's Y. Finally, having constructed the matrix X and the vector Y, we then just compute theta as X'(1 X) x X'Y.