{"id":16575,"date":"2019-12-31T19:21:34","date_gmt":"2020-01-01T00:21:34","guid":{"rendered":"https:\/\/bangla.salearningschool.com\/recent-posts\/?p=16575"},"modified":"2020-02-08T09:42:42","modified_gmt":"2020-02-08T14:42:42","slug":"part-4-some-basic-math-stat-concepts-for-the-wanna-be-data-scientists","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16575","title":{"rendered":"Part 4: Some Basic Math\/Stat Concepts for the wanna be Data Scientists"},"content":{"rendered":"

Part 4: Some Basic Math\/Stat Concepts for the wanna be Data Scientists<\/p>\n

Also for the Engineers in General<\/p>\n

Quadratic form<\/h1>\n

“In multivariate statistics<\/a>, if \"\\varepsilon\" is a vector<\/a> of \"n\" random variables<\/a>, and \"\\Lambda\" is an \"n\"-dimensional symmetric matrix<\/a>, then the scalar<\/a> quantity \"{\\displaystyle is known as a quadratic form<\/strong> in \"\\varepsilon\".
\n”<\/p>\n

Ref: https:\/\/en.wikipedia.org\/wiki\/Quadratic_form_(statistics)<\/a><\/p>\n

Please also check matrix related concepts. We will provide some matrix concepts at one point.<\/p>\n

“In mathematics, a quadratic form is a polynomial with terms all of degree two. For example, is a quadratic form in the variables x and y. Wikipedia<\/a>”<\/p>\n

”
\n\"4x^2is a quadratic form in the variables x<\/em> and y<\/em>. The coefficients usually belong to a fixed field K<\/em>, such as the real or complex numbers, and we speak of a quadratic form over K<\/em>.”<\/p>\n

“Quadratic forms are not to be confused with a quadratic equation<\/a> which has only one variable and includes terms of degree two or less. A quadratic form is one case of the more general concept of homogeneous polynomials<\/a>.”<\/p>\n

Ref: https:\/\/en.wikipedia.org\/wiki\/Quadratic_form<\/a><\/p>\n

Quartic function<\/h1>\n

”
\nThis article is about the univariate case. For the bivariate case, see Quartic plane curve<\/a>.
\n\"\"<\/a>
\nGraph of a polynomial of degree 4, with 3 critical points<\/a> and four real<\/a> roots<\/a> (crossings of the x<\/em> axis) (and thus no complex<\/a> roots). If one or the other of the local minima<\/a> were above the x<\/em> axis, or if the local maximum<\/a> were below it, or if there were no local maximum and one minimum below the x<\/em> axis, there would only be two real roots (and two complex roots). If all three local extrema were above the x<\/em> axis, or if there were no local maximum and one minimum above the x<\/em> axis, there would be no real root (and four complex roots). The same reasoning applies in reverse to polynomial with a negative quartic coefficient.<\/p>\n

In algebra<\/a>, a quartic function<\/strong> is a function<\/a> of the form<\/p>\n

\"f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e,\"<\/p>\n

where a<\/em> is nonzero, which is defined by a polynomial<\/a> of degree<\/a> four, called a quartic polynomial<\/strong>.<\/p>\n

Sometimes the term biquadratic<\/strong> is used instead of quartic<\/em>, but, usually, biquadratic function<\/strong> refers to a quadratic function<\/a> of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form<\/p>\n

\"f(x)=ax^{4}+cx^{2}+e.\"<\/p>\n

A quartic equation<\/strong>, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form<\/p>\n

\"ax^{4}+bx^{3}+cx^{2}+dx+e=0,\"<\/p>\n

where a<\/em> \u2260 0.<\/p>\n

The derivative<\/a> of a quartic function is a cubic function<\/a>.<\/p>\n

”<\/p>\n

Ref: https:\/\/en.wikipedia.org\/wiki\/Quartic_function<\/a><\/p>\n

Quartic plane curve<\/h1>\n

Bivariate case<\/p>\n

”<\/p>\n

A quartic plane curve<\/strong> is a plane algebraic curve<\/a> of the fourth degree<\/a>. It can be defined by a bivariate quartic equation:<\/p>\n

\"Ax^4+By^4+Cx^3y+Dx^2y^2+Exy^3+Fx^3+Gy^3+Hx^2y+Ixy^2+Jx^2+Ky^2+Lxy+Mx+Ny+P=0,\"<\/p>\n

with at least one of A, B, C, D, E<\/em> not equal to zero. This equation has 15 constants. However, it can be multiplied by any non-zero constant without changing the curve; thus by the choice of an appropriate constant of multiplication, any one of the coefficients can be set to 1, leaving only 14 constants. Therefore, the space of quartic curves can be identified with the real projective space<\/a> \"{\\mathbb. It also follows, from Cramer’s theorem on algebraic curves<\/a>, that there is exactly one quartic curve that passes through a set of 14 distinct points in general position<\/a>, since a quartic has 14 degrees of freedom<\/a>.<\/p>\n

A quartic curve can have a maximum of:<\/p>\n