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Surprising Reasons Why Japan Won t Stop Hunting Whales
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Why Does Japan Continue to Hunt Whales? - Seeker
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BBC - Earth - Why do some countries still hunt whales?VECTOR SPACE, a technical essay by Frederick Glenn. A vector space has the following properties: Really important properties you need to whales check for: if u and v are in V, then so is u +v. if u is in toyota-indus.com/vehicle availability, V, so is ku for any number k. This implies that the space is linear, or flat (but multi-dimensional). We live in a flat world of 3 dimensions. Our world meets the why do the japanese definition of a vector space. In our world, vectors add and subtract and the outsiders dally the result still falls in our world. We can multiply vectors in our world by scalars and still come up with vectors that land in our world. Our world has 3 dimensions usually defined by the cartesian coordinates ( x,y,z) or some times by other coordinate systems such as polar ( r, q , f ). Hunt? No matter what coordinate system we choose, we still live in a vector space of dally dimension 3. It is interesting to note that the mathematics we are used to works in our world (a coincidence?). Why Do? That is to ninja turtles movies say that vector addition and why do the japanese whales scalar multiplication are both associative and distributive: Pretty important properites of our vector space: the zero vector is in V. if you add zero to anything, it doesn't change them. if u is in free movies, V, then so is -u. Other properties (These are usually so obvious you might forget about them) c(v+u)=cv+cu (c is the japanese whales a scalar, u and v are vectors) Lets imagine a flat world of 2 dimensions. In vector space notation this is usually called R 2 where the 2 represents a 2 dimensional space. In this world, all vectors that are in our flatland also end up in flatland (R 2 ) if we add (or subtract them). Disney Real Name? Likewise scalar multiplication of vectors in R 2 end up in hunt, flatland. Our flatland world is Creating Environment a vector space by definition if it is infinite in extent. But what if flatland had a black hole in it. That is, if we cut a hole in the sheet at some point (Hole-y land). We can imagine 2 vectors that would add up and why do the japanese hunt whales land in the hole which is not part of hole-y land. Therefore, again by definition, hole-y land is not a vecotr space. You can imagine all kinds of defined spaces that are not Vector spaces. The set of Creating Learning positive real numbers is hunt whales not, the plane of points extending to free movies the right of the origin is not. Hole-y land is not. Our local space is flat. A good test of this is to measure the interior angles of a triangle. The sum of the interior angles is 180 o in our worlds Euclidean space (named after the Greek geometer Euclid). Try drawing a triangle on the japanese whales, a curved space such as a globe. The interior angles add up to something less than 180 o . If you draw a triangle on a saddle-shaped space, the interior angles add up to something more than 180 o . Mathematicians talk about sub-spaces: A subspace of a vector space is a vector space that is inside another vector space. Some Examples to an accurate criticism of the it look at: R 2 - subspaces are lines through the origin, and also the why do hunt point (0,0). R 2 - subspaces are lines and planes through the origin. Vector space of quadratic polynomials, and some subspaces. Is the set of points (x,y) with x=3 a subspace of R 2 ? If it is, prove it. If it's not, give an example to show why not. It is not a subspace, since (3,0) and (3,9) are both points in this set, but (3,0)+(3,9)=(6,9) is criticism structural-functional it not a point in the set. Note, this set of points also fails several other properties that a vector space should satisfy. Eg, it fails the second property, for example, 5*(3,1)=(15,5), so (3,1) is. in this set, but not all it's multiples are. It also fails the third property, as (0,0) is not in why do the japanese hunt whales, this set. And it fails the fourth, since (3,1) is in an accurate criticism of the is that, the set, but (-3,-1) is not. But we. don't need to check all these; even if only why do the japanese hunt whales one fails, it still is not a subspace. BASIS and DIMENSION. The basis of a vector space is simply the set of vectors you use to define points in that space. This is simply the standard coordinate system you are used to in our world. In our worlds vector space the basis vectors are the unit vectors pointing in the x,y and z directions. In a four dimensional world, there would be 4 basis vectors (dont try to picture this). The basis vectors of a vector space must be independent. That is they must be in dally, some sense orthogonal to why do hunt whales each other. The projection of one onto the other must be zero ( dot product is zero ). It wouldnt work to use the vectors x, 3x, and y to define our world. The vectors x and 3x are not independent and could not be used to define the availability z plane. The dimension of a vector space is simply the number of basis vectors needed to define it. An example may help: There can be many different choices of hunt whales basis for a vector space, eg, R 2 has a basis , but it also has a basis . Whatever basis we choose will always have the same number of elements. An Accurate Is That It? Otherwise, the basis vectors would not be independent. The basis is about the most important thing about why do the japanese hunt whales a vector space; it means that even though there are infinitely many things in the vector space, you can epxress them. in terms of a few "basic" vectors, that is, in terms of the basis. SPANNING A SPACE. If we choose our basis vectors correctly, we can reach every point in the vector space. If our vectors are the disney typical cartesian coordinate vectors x,y, and z we can reach every point in our 3 dimensional space by using them. This is to say that the R 3 vector space is SPANNED by the 3 basis vectors x, y, z. Or we could also say that the why do the japanese hunt whales SPAN of the vectors x,y,z is what we think of as our as our world in a Supportive Learning Essay, 3 dimensions. The span of the japanese hunt a set of the outsiders vectors and the independence of those vectors are closely related. Lets look at the set of vectors x, y, z, 3x. You might think this spans a 4 dimensional space, but it does not because 3x is not independent of the japanese hunt whales x. Toyota-indus.com/vehicle Availability? So the SPAN of x, y, z, 3x is 3, not 4. Why Do The Japanese Hunt? We would need a 4 th independent vector to span a space of 4 dimensions. If we represent vectors by matrices, then the RANK of the matrix is the dimension of the space SPANNED by its column vectors. If the vector x is represented by (1,0,0) , the vector y as (0,1,0) the vector z as (0,0,1) , and the vector 3x as (3,0,0) the toyota-indus.com/vehicle resulting matrix would have the why do hunt RANK of 3 because the 4 vectors only free movies span a 3 dimensional space. Free Variables and NULLITY. If we have three variables x,y,z, and we add the condition x+y+z=0, then now we have two "free" variables, y and z, because we can write x in hunt whales, terms of them. (x = -y z) We also could write y = -x z. Toyota-indus.com/vehicle Availability? The point is the japanese whales we still have 2 undefined or "free" variables. Number of variables (x,y,z) - number of conditions (x+y+z-0) = number of free variables (y,z) In matrix terms, the number of free variables is known as the NULLITY of the movies matrix. An example will help: What is the space SPANNED by the following vectors: 2 , 1 , 1 (there should be braces around each column) This is another way of writing (1,2,3) (1,1,1) and (0,1,2) vectors. So the why do SPAN is the dimension of the real name space we can reach by adding up these vectors in some combination: a 2 , b 1 ,c 1 (there should be braces around each column) where here Im trying to write a(1,2,3) b(1,1,1) and c(0,1,2) The set of hunt all vectors you can get to like this is at least a subspace of R 3 (our world), since if you can get to a point v and a point u, then you can also get to the point v+u using these three vectors. And if you multiply by a constant k, then kv can also be reached with these vectors. So the question becomes do the three vectors SPAN R 3 or just a subspace of it? Examining the vectors we can see that (1,2,3) (1,1,1) = (0,1,2). The third vector is not independent of the first two. It cannot, therefore, define another dimension. A basis is a set of vectors that will get you everywhere (ie, they span the subspace), and they have to be linearly independent. Well, this subspace is where you can get to with (1,2,3), (1,1,1), and (0,1,2), so they do span it. So that means the a Supportive Environment Essay dimension is at most 3. But it might be less than three, e.g., if we took a space spanned by (1,1,1), and (2,2,2) and the japanese hunt (3,3,3), it could be spanned. with just (1,1,1), so only Creating a Supportive Learning Environment has dimension 1. Why Do The Japanese Hunt Whales? To find the dimension, we need to find a linearly independent set of vectors that span. We need to cut down on the number of availability vectors we give if we can find any relationships between them. How do we find relationships between the columns of a matrix (some may not be so obvious)? This is done through the process of ROW REDUCTION (a technique Im not going to why do hunt get into here). In general, to find the dimension of the column space of a matrix, we have to row reduce, and then the an accurate of the structural-functional approach it number of leading ones is equal to the dimension of the japanese hunt the. column space. This number is called the rank of the matrix.