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Why linear algebra is called linear - you mean what is significance of the word linear in linear algebra?
Linear algebra deals with mathematical transformations that are linear. By definition they must preserve scalar multiplication and additivity.
T(u+v)= T(u) + T(v)
T(R*u)=r*T(u) Where "r" is a scalar
For example. T(x)=m*x where m is a scalar is a linear transform. Because
T(u+v)=m(u+v) = mu + mv = T(u) + T(v)
T(r*u)=m(r*u)=r*mu=r*T(u)
A consequence of this is that the transformation must pass through the origin.
T(x)=mx+b is not linear because it doesn't pass through the origin. Notice at x=0, the transformation is equal to "b", when it should be 0 in order to pass through the origin. This can also be seen by studying the additivity of the transformation.
T(u+v)=m(u+v)+b = mu + mv +b which cannot be rearranged as T(u) + T(v) since we are missing a "b". If it was mu + mv + b + b it would work because it could be written as (mu+b) + (mv+b) which is T(u)+T(v). But it's not, so we are out of luck.
What else can I help you with?
What does Pearson's linear correlation coefficient measure?
Strength and direction of linear relation. Closer to 1 is positive linear association, closer to -1 is positive negative association and closer to 0 means no linear relation. Remember that 0 does not mean that there is no relation - just no linear relation.
Why is the sample standard deviation used to derive the standard error of the mean?
the sample mean is used to derive the significance level.
What is the normal probability plot of residuals?
When you use linear regression to model the data, there will typically be some amount of error between the predicted value as calculated from your model, and each data point. These differences are called "residuals". If those residuals appear to be essentially random noise (i.e. they resemble a normal (a.k.a. "Gaussian") distribution), then that offers support that your linear model is a good one for the data. However, if your errors are not normally distributed, then they are likely correlated in some way which indicates that your model is not adequately taking into consideration some factor in your data. It could mean that your data is non-linear and that linear regression is not the appropriate modeling technique.
What does a correlation of -0.9 mean'?
as one variable increases the other variable decreases
Which situation would most likely employ linear regression techniques?
b. Calculating the mean cost of one individual unit in a production run of 10,000 units
What does linear mean in Algebra?
Linear means a straight line.
What do you mean by eigen value and eigen function?
In linear algebra, there is an operation that you can do to a matrix called a linear transformation that will get you answers called eigenvalues and eigenvectors. They are to complicated to explain in this forum assuming that you haven't studied them yet, but their usefulness is everywhere in science and math, specifically quantum mechanics. By finding the eigenvalues to certain equations, one can come up with the energy levels of hydrogen, or the possible spins of an electron. You really need to be familiar with matrices, algebra, and calculus though before you start dabbling in linear algebra.
How will you remember the properties of Algebra?
There are many different areas within algebra: linear algebra, algebraic structures, algebraic geometry, vector algebra and so on. Some properties are valid in only some of these and not in others. You need to understand what the properties mean and perhaps keep in mind one or two examples where the property is valid.
What does is mean in algebra?
In Algebra, "is" means Equal (=).
What does algebra mean in English?
Igual>>> ALGEBRA
What does and mean in algebra?
"And" in algebra usually means addition.
What does algebra 1A mean?
It usually refers to an introductory algebra class.
What does difference mean in algebra?
It mean to Subtract (-)
What does D mean in algebra?
D can mean anything, it's only substituting a number that you have to find out. That's how you do basic algebra
What is it called when you add a number to both sides of a math question?
do you mean math equation? If you add a number to both sides of an equation you do not change it. That is called algebra
What do you mean by algebra?
algebra involves equations with numbers a variables and your goal is to solve for the variable
What does the word Algebra mean in English?
If your in English Class it Means that you should be in your Algebra Class.
