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Bruno Tolentino
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If the vector r is (x,y), so, what is the vector θ? BY THE WAY is (y,-x) ?
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I didn't notice the "(y, -x)"! If a vector is given by r= (x, y) then its length is |r|= [itex]\sqrt{x^2+ y^2}[/itex] and the angle it makes with the x-axis, it that is what you mean by "[itex]\theta[/itex]", is given by [itex]arctan(y/x)[/itex] as long as x is not 0, [itex]\pi/2[/itex] if x= 0 and y is positive, [itex]3\pi/2[/itex] if x= 0 and y is negative.Bruno Tolentino said:If the vector r is (x,y), so, what is the vector θ? BY THE WAY is (y,-x) ?
HallsofIvy said:I didn't notice the "(y, -x)"! If a vector is given by r= (x, y) then its length is |r|= [itex]\sqrt{x^2+ y^2}[/itex] and the angle it makes with the x-axis, it that is what you mean by "[itex]\theta[/itex]", is given by [itex]arctan(y/x)[/itex] as long as x is not 0, [itex]\pi/2[/itex] if x= 0 and y is positive, [itex]3\pi/2[/itex] if x= 0 and y is negative.
Given a vector (x, y), the vector (y, -x) is the result of rotating (x, y) through an angle of [itex]pi/2[/itex] radians.
Vector theta represents a mathematical concept used in linear algebra and statistics. It is a vector that contains the parameters or coefficients of a statistical model, often used in regression analysis.
The calculation of vector theta depends on the specific statistical model being used. In general, it involves finding the values of the parameters that best fit the data and minimize the error between the model and the observed data.
A vector theta contains multiple values, while a scalar theta only contains a single value. In statistical models, vector theta is often used to represent multiple parameters or coefficients, while scalar theta may represent a single intercept or slope.
In machine learning, vector theta is used to represent the weights or coefficients for a given model. These weights are adjusted during the learning process to minimize the error between the predicted outputs and the actual outputs.
Yes, vector theta can contain negative values, depending on the statistical model being used. In some models, negative values for the parameters may indicate a negative relationship between the variables, while in others it may have a different interpretation.