Vektheri e fapaneng
Pendahuluan
Lipalong le fisiks, khopolo ea li-vector ke ea bohlokoa 'me e sebelisoa khafetsa lits'ebetsong tse fapaneng, ho tloha fisiks ea khale ho ea tlhahlobong ea data ea sejoale-joale. Khopolo e 'ngoe e khahlisang thutong ea li-vector ke vector e fapaneng. Sehlooho sena se tla hlalosa hore na vector e fapaneng ke eng, mokhoa oa ho e bala, le ts'ebeliso ea eona bophelong ba letsatsi le letsatsi le saense.
Vekthara ke eng?
Pele o hlahloba mohopolo oa li-vector tse fapaneng, ho bohlokoa ho utloisisa hore na vector ke eng. Vector ke ntho ea lipalo e nang le boholo le tataiso. Ho fapana le li-scalar, tse nang le boholo feela, li-vector li khetholloa ka likarolo tse peli tse kholo: boholo (kapa bolelele) le tataiso. Li-vector hangata li emeloa e le metsu sebakeng sa mahlakore a mabeli kapa a mararo, moo bolelele ba motsu bo bontšang boholo ba oona le tataiso ea motsu e bontšang tataiso ea oona.
Mongolong wa dipalo, divekthara hangata di ngolwa ka sebopeho sa \( \mathbf{v} = (v_1, v_2, …, v_n) \), moo \( v_1, v_2, …, v_n \) e leng dikarolo tsa vekthara ka motheo o itseng.
Tlhaloso ea Vektha e Fapaneng
Vekthara e fapaneng ke vekthara e nang le lehlakore le fapaneng le vekthara ea pele, empa e na le boholo bo tšoanang. Haeba re na le vekthara \( \mathbf{v} \), joale vekthara ea eona e fapaneng ke \( -\mathbf{v} \).
A re re \( \mathbf{v} = (v_1, v_2, …, v_n) \), ebe vekthara e fapaneng ke \( -\mathbf{v} = (-v_1, -v_2, …, -v_n) \).
Mohlala, haeba \( \mathbf{v} = (3, 4) \), joale vekthara e fapaneng ke \( -\mathbf{v} = (-3, -4) \).
Matlotlo a Li-vector tse fapaneng
Litšobotsi tse ling tsa bohlokoa tsa li-vector tse fapaneng li kenyelletsa:
1. Boholo bo Tšoanang: Boholo ba vector le phapang ea eona lia tšoana. Haeba \( \|\mathbf{v}\| \) e le boholo ba vector \( \mathbf{v} \), joale \( \|-\mathbf{v}\| = \|\mathbf{v}\| \).
2. Ho eketsa lefela: Ho eketsa vekthara ka tsela e fapaneng ho tla hlahisa lefela vekthara. Ke hore, \( \mathbf{v} + (-\mathbf{v}) = \mathbf{0} \).
3. Tsela e Fapaneng: Vekthara e fapaneng e na le tsela e fapaneng le vekthara ya pele. Haeba vekthara \( \mathbf{v} \) e supa leboya, jwale \( -\mathbf{v} \) e tla supa borwa.
Mokhoa oa ho Bala Li-vector tse fapaneng
Ho bala vekthara e fapaneng ho bonolo haholo. A re re re na le vekthara \( \mathbf{v} = (v_1, v_2, …, v_n) \). Ho fumana vekthara ea eona e fapaneng, re fetola feela letšoao la karolo ka 'ngoe ea eona:
\[ -\mathbf{v} = (-v_1, -v_2, …, -v_n) \]
Mohlala, haeba \( \mathbf{v} = (5, -3, 2) \), joale vekthara e fapaneng ke \( -\mathbf{v} = (-5, 3, -2) \).
Litšebeliso tsa Vektara e Fetohileng
Khopolo ea li-vector tse fapaneng e na le lits'ebetso tse ngata masimong a fapaneng. Mehlala e meng ke ena:
1. Fisiks
Fisiks, hangata li-vector tse fapaneng li sebelisoa ho hlalosa matla a hanyetsanang kapa ho potlaka. Mohlala, tlhahlobong ea motsamao, haeba ntho e tsamaea ka lehlakoreng le itseng, matla a khohlano a sebetsang holim'a ntho a tla ba le tataiso e fapaneng le tataiso ea motsamao. Vector ea potlakang ka lebaka la matla a khoheli a sebetsang holim'a ntho e oelang ka bolokolohi le eona e na le vector e fapaneng haeba re nka hore tataiso e fapaneng e ntle.
2. Tsamaiso ea Likepe le Liroboto
Ha ho tsamauoa, vekthara e kgutlelang morao e sebediswa ho bala tsela ya ho kgutla. Mohlala, haeba roboto kapa koloi e tsamaya ho tloha ntlheng ya A ho ya ntlheng ya B ka vekthara e itseng, ho kgutlela ntlheng ya A, e tlameha ho tsamaya ka vekthara e fapaneng le vekthara e sebediswang ho ya ntlheng ya B.
3. Litšoantšo tsa Khomphutha
Litšoantšong tsa khomphutha, li-vector tse fapaneng li sebelisoa bakeng sa ts'ebetso ea mabone le moriti. Haeba mohloli oa leseli o tsoa lehlakoreng le itseng, vector e fapaneng ea lehlakoreng leo e sebelisoa ho bala meriti le lipontšo holim'a bokaholimo ba ntho.
4. Tlhahlobo ea Lintlha
Tlhahlobong ea data, livektha tse fapaneng li sebelisoa li-algorithms tse fapaneng tsa ntlafatso. Mohlala, ho theoheng ha gradient, ho fokotsa mosebetsi, re tsamaea ka lehlakoreng le lebe la gradient ea mosebetsi oo, e leng vektha e fapaneng ea gradient.
Qetello
Li-vector tse fapaneng ke mohopolo o bonolo empa o le molemo haholo lits'ebetsong tse fapaneng tsa lipalo le tsa mahlale. Ka ho utloisisa mokhoa oa ho bala le ho sebelisa li-vector tse fapaneng, re ka sekaseka le ho rarolla mathata habonolo ho fisiks, ho tsamaea, litšoantšo tsa khomphutha le tlhahlobo ea data.
Kutloisiso e ntle ea li-vector le li-inverse tsa tsona e bula menyetla e mengata ea ho rarolla mathata a lefats'e la nnete le ho nts'etsapele mahlale a macha. Joalo ka likhopolo tse ngata tsa lipalo, botle le molemo oa li-inverse tsa vector li lutse bonolo ba tsona bo tebileng le ts'ebeliso e pharaletseng.
