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Linear Functions © Lineaw meang Straight. * A linear fimelion te o straight line. © A Ungar anaph represents a linean {inction. Linear Functions A Function ig Special relationship wlan eae input has on output. — A function is offen written as - (x) where x {g input $ Pexyex ’ Results Ton Pex) =x ‘ x y =e if 4 yeh at 9 9: Ne ieee) 2) 3 yo*=3 4 4 y= x24 5 5 Yes et y Box a2 Se ax 24 yeas y =2x=8 y= 2x = to “y oats # 5x= SY Phelps (S- | Linear Regnegeton : i A Linear vegnession tries to model the telalionchip a two variables by Fitling a linear graph one variable Gd is Qongidened lo be dala, and the Other (y) is Goneidered lobe dependent. For example , a. Linear Regnession Con be amodel to welate the price of house Lo their Size, |, Lineom [east Squares | Unean algebra tv used to Solve Linear Equations. ; Lineom Least Squares (LS) tg a Get a? : fiomulotions &p Solving Statistical problems involved in Linear Regression. BD | theap Algebra — “i Linear Algehna is the branch My mathematics that | Concerns linear equations Cand linear maps) and | their mepregentations in. Veelop Space and through | matnices. J, Linear Algebra igeone oPthe moe! aoe part fon amochine Leaping: 444 Sealans b oIn linear algebra, ou Scalar iS Single number. x alk | Vectors are 1-dimentional Aprays. | Vectors hove a Magnitude anc: & Diveelion. | Vectore typically deseribes Molion op Force. | i | Vector Notation vector 2 con. be yillen in many wae. The most Common ome : air: Y= ae oe (al foes t V ms 2) ectop -a ts the opposite of +0. is meang that vector a and vector - a. hos the same mognitude in opposite divections + ip Cole modified by adding. Subtracting, anultiply ing a Scalow Gnumber) ee all the Vv eclor volues :- \ force is avertor, 7 Force ig a. vector with » Magnilude and a Direction. | Matrices Me N vrolnixzS Set of numbers. A matvix ts on Rectangular Aymay. A matnix ig avranged in Rows and Columns, Matrix Dimensions ig Matnix hag 1 vous ane 3 columns * ic= [2 53] The Dimension of the matniy ae C103). This matynix has 2 wows ‘bid: Geol ann: a=] ae op as lhe diwengiga or the molnix ig (2x8), A a Matix hag equal diagonal bane ane | an ero on the na Tt a wel Ly any malt withthe identity ‘arolrix, j ult equals the original. | Malrices ane orate iP each. lina corres pond: | Bas ‘ eas me 74) la 7 | Nega: Te of we 18 eagy lo undepstand + ay a A | a ees ina Matrices two motmices levees Same dimension, wecan m! \ Css ayeleiwe Ja) Ie ibe oi u 7 les al* |e 2 4 t Lie ies ie ial dimension, tue Con act them: Pied 24 ond Wren add the ree af 8 eis : Nae oh eit OR ORL “ GM 26 | ee = | Lxnt 2x24 3x2 = 42. 3 Sa 25 xg + 2x34 3X 49 Tensor N\ Tengop tg a N-dimengional Malnix : * {| Sealeae te a O-dimensconal tensor © fi veclor ig. 4- dimensional Lengo * f\ Madnix ig a 2- dimensional tensor A Tengor (sa generalization of veclon¢ and Malnizes bo higher dimensions. Sealanr Vector(s) 4 | [1-2 3] a ; Mattnt x Tensor ee tesa Led [en sor Ranks ‘The tumben of dinecliong a tensor dan. have tne N- dimensional Space, is Called the Rank ofthe Lense». The Rank ts denoted R. A geolan WS a. single peoneen!) *Thhae 0 fixes ° Tt has a Rank of 0 * tt is a O-dimensional Tenson A veelep ts an appa of mumbens, ett hag 1 fAxts © Tt hag aRanle off 3 © Thea tedimensienal Tensor A Matnix ts a 2-dimensvonal array. o Tt hag 2 Axia e Tt has 5 Ranleeh 2 eo Itiga 2- dimensional ‘TenSor Re al Tensors Technically, all of the above ame tensops, but when we Speak of Lensong, we genevally speak of matnices wilh dimension. larger than 2(R*2), 
